There are lots of answers to the problem of which class to choose in Baldur's Gate but, truth told, any class can complete the game. Of course, that said, there are some classes that are better than others and in order to demonstrate the point, I'll give you a quick list:
1) Thief - lots of NPCs in the saga have thief levels and while the skills are absolutely necessary in BG1, there is always someone readily available to disarm traps and unlock doors and chests.
2) Cleric - good healing is hard to come by with the best healer by far being evil. Fortunately, potions and the rest are incredibly common meaning that really all you need is a rod of resurrection and whatever healing spells your party can otherwise muster.
3) Fighter - Every other character in the game has fighter levels. While it's one of the easiest classes to play it's often the least useful. If you play a fighter, take a kit.
4) Mage - Pure mage is kinda garbage - grab a specialty if you want to go this route. At low levels you're the weakest member in the party but by the end of BG1, you're more or less an unstoppable killing machine.
5) Druid: Not a bad class but it has numerous problems. Basically, it's not a particularly great cleric, and not a great fighter. Still, you get adequate summons and shape shift is good enough to make it a viable class. Probably not worth taking all told.
6) Ranger: Basically a more combat oriented druid. You get cleric spells in the long run but not enough of them to really make it worth your while. The only kit worth taking here is archer.
7) Sorcerer - You get more spells per day and, notably, you simply get a pool of spells per level to cast. This gives you tremendous flexibility in how you use your daily spells but you have to draw from a limited spell list. Generally used as a pure glass cannon.
8) Bard - A class that is part thief, part fighter and part mage. It can fill any role needed in the party in a pinch it's just that it won't do it well. The leveling system is such that the weakness of the bard as a spell caster won't become apparent until Baldur's Gate 2 (bards gain levels much faster than mages and as such they maintain a sort of advantage until mages can cast level 5 spells) but in the long run, it isn't a great class. THACO isn't good enough to hit reliably in physical combat, they're sorely outclassed by mages in the long run, they aren't durable or proficient in toe to toe combat and they don't have access to the most important thief skills. Bards are still viable, but you're best served taking a kit like Skald (for the song) or Jester.
9) Paladin - Honestly a great class all around with strong abilities in every situation. You're forced into being lawful good and if you don't follow this path you can lose your status as a Paladin. If you choose this, it's probably best to choose a kit like Inquisitor which trades ability to fight at range with the ability to make some of the most annoying magic in the game a thing of the past.
10) Cleric - Actually shockingly good at close combat thanks to spells like Draw upon holy might and ability to wear heavy armor. Can easily support party from the thick of the action or from the rear lines. The only disadvantage is a very limited selection of weapons and an inability to really specialize in said weapon selection.
11) Barbarian - Similar to the fighter in most ways. A barbarian won't have as much skill with a weapon as a fighter no can they wear the heaviest armors. In exchange, they get more HP (they gain up to 12 HP per level versus the fighter's maximum of 10 [+ bonus HP from your constitution]) and have access to rage which offers a lot of boosts to combat abilities and a lot of immunities in exchange. This is probably the easiest class to play.
In the very long run, the most useful pure class is probably paladin though any class is fully viable if you play well. If you want to power game, there are certainly options.
Dual Class - This is tricky in Baldur's gate since you have to basically know what stats you want when you create your character. You've got to have 15 points in the primary stat of your starting class and at least 17 points in the primary stat of your ending class. For example, this means if you want to be a thief/mage you'll need to have at least 15 dexterity and 17 intelligence. Worse still, when you switch classes, you lose access to all the abilities of your starting class until you reach the same level as your starting class plus one additional level. Thus a thief mage that chose to multiclass at level 9 has to gain 10 levels as a mage before they can again pick locks and search for traps or backstab
Multiclass - Non-humans cannot dual class and instead multiclass. When you multi-class, you basically split your experience across all of the classes simultaneously. This effectively means a multiclass thief/mage will have lower thieving skills than a pure thief (backstab multiplier, skill at finding and disarming traps, etc) and fewer spells of lower level than a pure thief or pure mage. Also, you can't choose specific kits or specialties when you multi-class which means you're forced to take the base kit.
From a power gaming perspective, Dual Classing is generally the better way to go in the very long run but, inevitably, this means your main character is remarkably weak for quite a long time compared to a specialist character. There are, of course, lots of combinations you can choose for multi/dual classing but only a few of them really stand out:
Fighter/Mage - You gain far more HP and pure combat ability than a mage has while simultaneously getting access to a pile of mage spells. While just about any fighter/mage kit is good, the Kensai fighter kit stand out above the rest. The Kensai gains tremendous close combat abilities at the cost of not being able to wear armor and, considering the mage can't wear armor and cast spells anyhow, this is basically a non-issue. The Kensi/Mage is probably the most powerful combination in the game as it gives you a character easily capable of soloing the game if you know what you're doing.
Thief/Mage - The ultimate utility character, basically. Between the thief skills like trap finding and hiding and backstabbing and the pure firepower of the Mage, you have a tool for literally any situation. Still, the low HP and low THACO and low AC mean this character has to be carefully micromanaged to be truly useful. This is probably my favorite combination but it's also one of the hardest to play.
Fighter/Cleric - The cleric is, somewhat counter-intuitively, one of the most powerful combat classes in the game. It has access to a list of spells that are tremendously useful and can cast them while wearing heavy armor. Couple that with having a decent base THACO and having access to lots of buffs, it's a powerful class. The fighter levels give more HP and the ability to truly specialize in a weapon along with an even better THACO. Basically, this is a character than is easily a better fighter than a fighter for a limited duration that also has decent spellcasting abilities and some capacity to fight even without spells to sling. Like the Thief/Mage, it requires significant knowledge of the game's systems before it really comes into it's own.
Thief/Cleric - An odd mix considering a limited selection of items to take advantage of backstab, a low THACO and fairly low HP. Still, you have lots of tools for a given situation and you'll easily be able to fill a role adequately.
Fighter/Druid - Somewhat makes up for the weaknesses of the Druid (slow leveling, small selection of spells) and fighter (magic is you're bane in the long run) but all told isn't a great selection. Clerics have better spells and a pure fighter if far and away the better fighter.
Fighter/Thief/Mage - Basically a different route to the bard. You will never be the best choice for any particular task (or even second best) but you do have ultimate versatility. This class, more than any other, requires specific knowledge about the rules.
Now that the text dump is finished, I can make it even easier. The simplest way to play the saga is as a pure character and on this front you have two standouts: The specialist Mage or the Paladin. The specialist mage has lots of spells per day (and, if you choose conjurer you don't really lose any useful spells ) and becomes tremendously powerful in the long run in spite of being physically weak. This necessarily requires that you constatly fiddle with memorized spells to ensure you have the right set of tools for a job. The Paladin, meanwhile, gets excellent durability, access to the most powerful weapon in the game, and even minor spellcasting. This requires more knowledge about the game than other classes. You're last choice is the Barbarian which is far and away the easist class given that you are basically a more durable fighter without access the peak of skill a fighter offers.
Of the multi-class options, the fighter mage is the most forgiving. You have a tool for just about every problem and if push comes to shove you're no slouch in melee combat either.
For a first playthough, I'd probably recommend a paladin as my first choice, The combination of martial prowess and minor spell access simply makes perfect sense for the game. Failing that the brutally simple barbarian is an excellent choice. If you are concerned about long term power (and don't mind dealing with a dozen or more frustrating hours where you're playing as a weak and pathetic PC) any multiclass that includes a mage can be extremely potent. Of those combinations, the Kensai Mage has the most combat power while the thief/mage has the most useful utility. The fighter/thief/mage spreads it's bet across too many classes and thus you are stuck with a character without much skill in combat, insufficient abilty to sneak to attempt a stealthy solution, and an dramatically underpowered spell list This is an easy class to ruin and a hard class to play well.
Personally, were it my first time, I'd opt for a pure paladin. It's simple enough for anyone, has access to sufficiient spells to fill a pinch role as a spellcaster, and is incredibly durable. If you want to risk signifcant frustration in the middle, the kensai/mage is potentially one of the most powerful combinations in the long run.