I bought a cheap iPod Touch a couple years ago and was pretty disappointed with it. I mostly play action games and touch screen controls just don't work for me. At all. It's very difficult to pull off special moves in fighting games, and shmups usually have autofire enabled which makes it very difficult to maintain combos and multipliers if you're playing for high scores. Control might be easier with some practice, or on a larger screen device, but I'd much rather play on the PSP.

The only controller options I've seen are peripherals like the iCade or iControlPad. There aren't many games that support them and very few of them are major titles.

The only games that didn't leave me frustrated with the controls are swiping/flicking, cursor control, or tilt control games. Mostly puzzle, strategy, tower defense, pinball, etc. Found a few standout games like GeoDefense/GeoDefense Swarm, Real Racing 2, Chopper 2, Dark Nebula, etc but after trying 100+ games most of the others either left me frustrated with the controls or were so simple/basic that they weren't worth playing.

I'd also hoped to use the component output cable and play some of the iOS games on my TV but touch screen games require you to look at the screen and tilt screen games keep knocking the A/V cable out of the iPod. More disappointment.

Thankfully I went the cheap route and bought an older gen hand me down but you also need to beware of obsolescence with iOS devices. They have a fairly short lifespan until new release games stop supporting older gens. Even simple new release games aren't compatible with my '3rd gen' 8GB model. If there's a major processor or memory upgrade when they release 6th gen, you'll be stuck with the current game library. Forced obsolescence. My kids like Angry Birds but my 2009 release iPod won't even run Angry Birds Space.

If you really want to try one, I'd look for used/cheap initially. 3rd gen (32GB/64GB only) or newer. I think I found enough to like for the ~$100 total that I spent on the iPod and game purchases... barely.

What Tom said.