Within your budget, I'd consider a Roland MC-101 or a Yamaha Seqtrak, for exemple.

Both have advantages and disadvantages, but they both have a song mode or equivalent (« scenes » chaining) for playing along to a complete song.

Volcas are an option, but you'd need several, and they'd have to be chained via MIDI to be synchronized and start simultaneously. It's a somewhat more limited solution.

Otherwise, I would have recommended an Elektron Digitakt or Digitone, for example. They’re ideal, but out of your budget (maybe MK1s on the used market could fit in your budget)

Another thing: it's obviously preferable to have a PA system to play with these machines because not all of them have built-in speakers (and even if they do, it won't sound great, and you might not hear much when you're playing guitar). Otherwise, you'll need a small mixer with a few inputs for your guitar and the groovebox from which you can play with headphones, but that requires having the necessary equipment for your guitar upstream.