as a beginner i'd steer away from cichlids. i think they are beautiful but best left to the experts. i wouldnt have any just yet until i'm more experienced. tetras can be fin nippers, so be sure to have at least 5-6. they also need to be accimated really slowly. there are loads of tetras to choose from and i've had few problems with mine. the head and tail light tetras have a few spats between themselves, but dont bother the other fish, and the cardinals have started attacking the neon. for this reason only, i dont think i'd get tetras again. i dont like the stress of breaking up fighting fish and the damage they can do to each other!! i like harmony in my tanks! the penguin tetras havent shown any aggression at all and are much more timid prefering to hide behind plants and make me think they've disappeared!!
danios are about 2 inches at the most and very hardy and peaceful if in a group of at least 5. there are loads of varieties to choose from. the livebearers (platties, mollys, guppies, swordtails etc) are under 2 inches, are hardy and cheap and colourful and available everywhere and in a range of colours and patterns and are easy to breed if you want to go down that route and practice rearing fry. its easy to differentiate males/females, so if thats not for you, just go for all males. they wont fight. if you go for all girls, chances are they're already preg and will give you fry for the first few months, however, its highly likely they'll get eaten unless you give them somewhere safe to hide/grow up in. dwarf neon rainbow fish are hardy and about 2 inches. very colourful and pretty (photo of one in my link in my sig). i'd steer away from tiger barbs....i've heard they can be aggressive, and for that reason i personally wouldnt have any. cherry barbs however seem peaceful and they're under 2 inches too. most gouramis get very big, dwarf gouramis stay about 2 inches, but dont put with a betta. not many fish go well with a betta as they find the bettas fins irrisistable to munch on!
dont know if i've been any help, but we all choose dif fish for dif reasons. if we all had the same fish, life would be very dull! its all depends on how much research you do and what you're prepared to do if the fish do get aggressive...have you a spare tank to put a bad fish in?! (a naughty corner!). also i've never bought fish on the internet as the shipping is always so expensive (£40) seems the standard here, so would have to buy an awful lot of fish to make it worth while. so i go to the lfs and spend a few £ on fish with no shipping! also you can see the tank mates and whether they're happy, talk to the owner and see how much the do/dont care for fish. internet fish often have guaruntees though where you take a photo of fish if dead on arrival and they'll refund, but they wont refund the shipping. so i'd still be £40 down even if evey fish was refunded!! again, up to you. prob more choice on internet, but its not for me. thats not to say it wont suit you. i think chickadee uses internet for fish buying.....she may be able to recommend some sites to use if you're in the US which is where she is too.
let us know what you decide! any help just yell! sorry to have rambled on a bit.....i do that alot!
have fun and enjoy your fish!
tan

by the way....if you have silver dollars, dont get real plants. they gobble them up!!

- just so you know!!!