You're in luck- Korg have a bunch of 16 step drum machines. Try the Volca Beats, they look perfect. Check this:
http://www.synthtopia.com/content/2013/ ... more-50589.
They're brand new with street prices as low as
US$150 (but that's the first I've seen). Use midi-in or the audio-in to sync with your other gear. Only really old drum machines from the 70s will lack sync functions.
Alternatively check out 2nd hand Electribes. The
ER-1 is probably the best bet for what you've said (it's all drums). The
EM-1 has drums & 2 synth parts, the
S (mk1 or mk2) is a sampler & the
ESX-1 is a sampler & has basic wavetable synthesis. All run midi out so you can sync low numbered SPs to them (202, 303, 404). Or if you have a Nintendo DS, get the DS10/DS10+/M01 synth- it comes with a nice 4 voice drum synth.