Luxman has made very nice class A amps for decades, Accuphase, Sungden, Pass labs, all these can be had used in your price range if you look and have time. Luxman L540-550-560 are Pure class A amps from the early 80's that are wonderful and can be had for $1k to $2k depending on the condition, the newer ones still may be out of that price range. you should be able to find an Accuphase use for that as well. not sure if pass's integrateds are in that range yet or not. You see a few Sungden integrates in that range as well but harder to find in some areas. then of course there is many tube class A amps but I'm not sure if that's the way your thinking. It really depends like others have said on the efficiency of the speakers you buy. Class A is going to like more then 90db 1w 1m. if you go much lower then 25wch then your into 94db and up. of course that's speaker depended but as a general rule that's a good place to start.
one other thing to consider is a class A amp is going to be like a space heater as they run flat out all the time and the high bias causes a lot of waist heat. so something to consider if your in a warm climate. I would not count out class AB like many have already suggested.
I do like the look of the kinki audio integrated seems to be a good deal for what you get.