I have a Korg AX1500g processor and a RC-20 Boss Loop Station and I want to buy a new amp. I'm looking for something that will work pretty well with these. I don't need powerfull amplification, I rather need good quality sound.

Any recommendations?

Also, I would apreciate if someone could explain to me how a digital processor influences the overall quality of the sound. And how do you pick your amp if you are using a digital processor?

Thanks in advance,
Well, it all depends on what music you want to play and how much cash you can spend. So?

You can either plug the processor into the front of an amp or use it's effects-loop if it has one - either method has advantages, but which one works best depends on what amp you use and for what. And before I start recommending amps, I'd need the above question answered.
Price ?
Used or new ?
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I have a budget of about 200-250$, and I'm not looking for a used amp.

I want to be able to play blues, progressive/psychedelic rock (Pink Floyd).
Does it need to cover band volumes well or is this just for home use?

Basically in this price range you're looking at modelling amps or smaller tube combos. With you owning a processor, there's not much of a point in going for the former - luckily the latter usually works great together with pedals/processors and sounds nice for blues as well as '60s and '70s rock music.

On the cheap and mainly for home use there's stuff like these:

For low volumes, these'll give you nice cleans, while they'll distort when turned up, and I think the distortion from them will be suitable for what you're doing, though you'll want to use your processor for stuff that is a bit gainier (or in situations where you can't crank the amp). The Vox and Bugera might be loud enough to play with a drummer (depends on the drummer and the room you're in a bit), while the VHT will probably not be loud enough.

If you want something that is louder, you will either have to 1) spend more cash, 2) look for a used amp or 3) get something that sounds worse but is more powerful - I'd strongly advise you not to opt for #3, buying shitty equipment never pays off.
I don't need it to cover band volumes, it will be mainly for home use.

Thanks a lot for the advice .