What do you like in an inexpensive tube integrated

I've been very pleased with my Audio Space AS-3i integrated. Its price new is about the same as your budget. They are rare on the used market though. Re sonics, there's a review in the back issues of UHF Magazine and I agree with what they say.

I haven't heard the Stingray but the reputation of Manley gear is unquestioned. Also the EL84 is a very nice-sounding tube.

I have heard the Rogue Cronus and thought it excellent. It did sound quite different from the tube amps I own, so FWIW do bear in mind that amps don't sound the same just because they use tubes.

Or, as in my case, you listen more with the second system because it's in a room which is always available, like a bedroom, whereas the main system is in a shared room like the living room.