Barbarian first, just because I like to smash stuff. After that I am not sure, I have 4 friends who play aswell and they are all different classes.
If you are a warrior do not just go for STR and VIT try and get some INT and global Resist bonuses on your gear. STR and VIT are your main stats but you will need intelligence to increase your resistance to all kinds of elemental damage, without this you will get wiped quickly on later difficulties.
Fury regen, attack speed and lifesteal are also nice to have on your gear.
Having played all 4 character classes I have to say the Monk is probably the easiest to win with. My Demon Hunter keeps getting her clock cleaned by Diablo. Yes I used a female character cause she's more interesting to look at. Who wants to look at dudes all day? My Demon Hunter is halfway through Nightmare. Haven't managed to finish any other characters yet. Working Barbarian now.
The witch doctor is just plain creepy. I mean.. jars of spiders?! Wizard isn't too bad either. You definitely need to level both of them up before attempting much.
The barbarian didn't really become fun for me until level 20 (I think) when I got the whirlwind that I loved from D2. Whirlwind was awesome for escaping from the middle of a throng while doing damage. Still haven't found any decent weapons for him but he does pretty decent damage with his skills regardless.
I have read the class boards about the classes on the Blizzard forums. As for difficulty in completing Inferno diffculty, the DH and wizard have the easiest time. From my reading, the monk and barb are having a harder time. I haven't put much attention into the WD. The reason is the wizard and DH can kite very well, and avoid the hits. The barb and monk have a harder time, and the configurations I have read for getting through easier are sword and board.
It looks like Blizzard is possibly going to tweak the monk in the future. Hopefully they do. My DH isn't through nightmare yet (Act 3 just about to get to Azmodan). I found that buying upgrades on the AH have helped my experience a lot. I only use the gold one, and my DPS at 49 is 1900ish. I explore every area full and I try and build upgrades through the blacksmith and jeweller as needed. I would say that since I started the use of the AH, the game has became significantly easier to play. The most I have paid for an upgrade is 50K. Typically I don't pay over 30K to better equip DH.