For skills, I'll go through each with my own experience:
Melee: I've never touched unarmed, so I know nothing of it. I always go for 2h blade now; the increased range is invaluable. Never use daggers; for stealth kills and general 1 handed usage, go for the longsword, for the increased range and damage; I don't know about range and the usefulness in general of blunt, since I prefer the aesthetic of blades in all games, Oblivion no exception. When I made a shield class I just went to 2h quickly: dodging an attack was more effective than reducing the damage taken.
With that, Armour: I Think it's up to personal opinion. Light armour is much easier to avoid attacks and swing in and out of range with melee attacks, while heavy armour will make you avoid less but take less damage from strikes, so they are in theory equal. Though I always found light armour better, even when specced into heavy.
Armourer: Get this to 50 quickly so you can repair enchanted equipment on the fly.
Marksman: Don't touch this, it's really underpowered in Oblivion. Go for melee stealth kills.
Lockpicking: Don't touch this skill. Find an average or above locked item, and just push the tumblers and watch. Sometimes, your pick will move up at the same speed as the tumbler. Most of the time, the tumbler will go faster. Once it reaches the top when the tumbler moves slowest, press activate, and it will lock. It takes a few times to get this, but then you can break very hard locks at just 5 skill without breaking a pick. http://bit.ly/pVUIYO Has a better explanation.
Acrobatics and Athletics: Both are annoying as hell to level for sure. Acrobatics I found to be not so useful, but athletics is a must for melee oriented characters who dodge in and out of strikes, as it primarily lets fatigue return faster while moving.
Sneak: Unsurprisingly awesome for sneaky classes, unfortunately invisibility makes it redunant, apart from the sneak attack bonuses.
Speechcraft: Boring and useless. Once you unlock the Arcane University, you can make an illusion spell to increase disposition by 100 for 1 second cheaply, and you just use that before talking to people, since it won't run out once dialogue starts.
Mercantile: Useless in my opinion, you quickly get more gold than you use. You can use an Arcane University spell with restoration to boost Mercantile to 100 to invest in a store for the extra 500g limit.
Restoration: I found this fairly useless beyond the boost attribute spells at 25 resto skill, using rest or potions is more effective.
Mysticism: After 25 to get soul capture, useless really, it's why its being absorbed into other skills in Skyrim.
Illusion: Apart from the replacement for speechcraft, fairly underpowered until the skill reaches 50, then it's fairly OP. You unlock paralysis (which you should only have for 3 seconds, just enough to make them go on the floor and thus have to spend time getting up again) and invisibility (which can be used in combat to escape combat) make many fights after a joke.
Alchemy: Don't spec into this; it will screw up your levelling. This will be your main money maker, just go a alchemy vendor, buy all the low priced ingredients, turn them into pots and sell them back for a profit. The prices increase dramatically as you get better apparatus. Buy healing potions from vendors though.
Alteration: I never found it useful. the unlock is redundant, My defence is generally maxed out at 85 even in light armour so that's pointless, I have trinkets for the other abilities.
Conjuration and destruction: I never liked these, because of mana restraints and whatnot. I switched to using melee weapons personally, but apparently at least destruction is super awesome. I personally preffered saving the mana for paralyse.
Attributes: Endurance is good to have high at the beginning because of how HP calculations work (it adds a tenth of your endurance as hp each level, decimals kept as floating numbers for later levelling). Strength is obviously good, but it can be enchanted on gear for extra inventory space. Personality is useless. Speed is obviously good, the best stat if you want a 2h dodging melee guy, or a stealth character (to get into range before the target turns round). Intelligence and willpower very similar, and it is down to calculations to which one is better, since a higher mana pool entails a higher mana regen. Agility is very useful to not get staggered and thus not get stabbed in the face with a 2h weapon. Luck doesn't seem that great but is something to go for once other useful attributes are used.
Last tidbits of advice: Enchant your gear with shield and strength, or if you have the skill for it, fire/frost/shock shell. The F/F/S shell also increase armour by the same amount (though it doesn't say) and generally are stronger than normal shields. The cap is 85. Unlock the Arcane university as early as possible.
