I owned & very much enjoyed first the Uno's purchased in about 2001 & then upgraded to the Duo's in 2003 which I kept for about another 6 years until I decided to try a pretty high end surround sound system based on Dynaudio Contour line of speakers. I was watching a lot of movies at that time as well as listening to music & only had room for one system. I know the Avant Gardes pretty well & they are very special & great in many ways.
I used an Art Audio PX25 SET power amp & an Aesthetix Calypso preamp w/ excellent results w/ a very good Basis table/ arm & a nice Naim CD player. The amp is 5 watts per side & more than enough power to drive the Duo's to loud volumes in a big room & sound great! It uses a special tube that not many have heard of (the PX25) which has a beautiful midrange & high end & w/ the powered subs of the Duo's, I don't really know about the bass. I think they are now very expensive ($17K) but might be in your price range for a used one? I would suggest that whatever amp you get, try to find one that is fully point to point wired so it can repaired by any good tech w/ a schematic years from now if needed.
Here's a few thoughts on the Duo's that might help regardless of what amp you wind up with:
1 - They are not easy to set up & get dialed in & expect this to take a while. Distances form boundaries, from each other, from you, toe in angle etc. all can have enormous effects on the sound!
2 - Getting the subs dialed in also takes patience w/ both volume & frequency selections. I sub's amps are very susceptible to hum & ground loops as I don't think the power supplies in them were that great. The original versions of these speakers had different subs which got improved after a few years, not sure which you have & I don't recall what the different sub models were called. I didn't have a power conditioner back then but one might help if this is an issue.
3 - The stock jumper speaker wires that go to the different drivers aren't great that came w/ the speakers & I had some custom ones made by a wire maker friend of mine that greatly improved the overall sound. I think even a decent wire from Audioquest would help out a lot.
BTW, I have since realizedI can't live w/o horn loaded speakers if I really want to enjoy music that sounds close to live as opposed to good "hifi" sound so I sold my surround sound system & got back into horns & tubes w/ Volti Audio Rivals & a Rogers High Fidelity integrated amp. Both are really good! Still have my Basis turntable set up (new cartridge) & now stream w/ an Innuos Zenith. Music is fun again!!