Boss RC-2 has stock beats. There are a couple pretty cool ones. You can turn the volume on the "guide beat" up and down or off. This little box is stuffed with features,so it can be a bit complicated. E2 HEAD RUSH
this page has some cool links to KT Tunstall doing her thing. The trick is the small mixer that allows the looper to capture the beat and the "base" or first track at the same time.
Drum machines and loopers inevitably drift apart unless locked together with a midi clock. So you are on the right track to get it in an all in one package. Something that can take a couple inputs at once.
Disclaimer: I'm a looper addict and I've failed to master the RC-2, the Akia, or the Digitech timebender. Not one to give up easily, I'll be picking up a Jamman today.
Looping turns out to be harder than it looks, but its a cool practice tool, and a merciless playback of your sound.