40K is the best for beginners, the rules for that are a bit less complex than fantasy, however fantasy as a game can be much more rewarding to play than 40K so it's a tradeoff i guess. I have both 40K and fantasy armies.
The basic rules can be gotten in one or two games such as the different phases and what to do in each of the phases, it takes longer to fully commit them perfectly to memory. But after a while it becomes second nature.
For 40K, the best army to start with is Space Marines. They are solid all rounders whose basic troops can go toe to toe with much harder things in other armies. They are also very tactical and versatile, however they don't really specialise in one particular style of play unless you choose a particular chapter such as Space Wolves who specialise in counter-attacking or Blood Angels who focus heavily on assault.
After that, you have Orks which are probably the next best starter army as they have pretty fun rules and focus on mobbing the enemy.
Eldar and Dark Eldar are for players who like having toolbox armies, in that each unit is specifically tailored for one type of enemy (see Eldar aspect warriors) and who like to play a fast paced game (Dark Eldar have some of the fastest transports in the game).
Tyranids are stupidly powerful combat focused aliens with a ton of rules that can annihilate an enemy force if you know what you're doing.
Tau are long range specialists, their ranged fire power is second to none.
Necrons are stupidly hard, stupidly tough with some really horrible special rules too but their weakness is high points cost and bad in combat.
Imperial Guard are the human army, standard weak men who die very easily but are supported by the most powerful tanks in the game and have strength in numbers. Some of their elite units are also very nice.
Chaos (Daemons and Space Marines) are basically Space Marines with some very nasty rules added, they also have support from Chaos Daemons such as Bloodletters and the Bloodthirster. There are four 'marks' of Chaos to choose from, or you can go undivided.
Grey Knights are like super powered Space Marines, they are ridiculously hard but have a high points cost.
Sisters of Battle are like women Space Marines. A little less tough but have some very nice tanks and special rules that make them a pretty scary force.
I personally have Eldar because i like having a squad of aspect warriors tailored to taking out standard infantry in one round of combat (Striking Scorpions) or a squad that can take out a tank without even breaking a sweat (Fire Dragons). Eldar are also supported by some of the most advanced weaponry in the game such as the D-Cannon. If an enemy model is caught in the blast of a D-Cannon, you only need to roll a 2 to wound, if you roll a 6 to wound, that model instantly gets taken off the board regardless of wounds or anything else. They also have wraithlords, I don't need to say anymore, just google them.
PM me if you want more info.