Alchemist isn't an Only-Expert class, but it's a bit of an oddball. Once you get used to the rules, go for it! A lot of the classes are like that, honestly.
personally, until you get the knack of the rules, what spells are useful...etc....Fighter/Barbarian is great for making "bad" rolls still OK, and having combat move quickly.
I want to also reinforce what Lamontius said - all of that is good advice. Playing a fighter reduces the amount of extra rules you need to know, it will maximize your ability to hit, and it's a great intro to the rules. Plus they have Ride as a class skill so there's no reason you can't get a mount.
What level are you guys starting at? If you're all going to be 1st level, how about just using pre-generated characters? That will take out a lot of the worries at 1st and get you guys rolling (literally!)
http://paizo.com/download/pathfinder/PFS-Pregens.zip