You should be able to pick up an Alesis HR or Roland (Boss) DR for that, or less.
Most of them will have some preset patterns, and you can program in pattern changes for fills and stuff.
It is MUCH more tedious to actually program beats yourself. Most have a "real-time" entry where you just tap pads, and also "step-entry" where you choose 1/4, 1/8, 1/16, etc. intervals, input a note, advance, input a note, advance, etc.
You could, say, input hi-hats every 1/16th to the measure, and input a snare every 1/4 in the measure.