Entry Level Tube Integrated Amps

I found that vintage Dynaco amps are very affordable when wetting your beak on tube amps. I've also tried a Prima Luna integrated amp and really liked that too.

Tubes are fun, rolling them can turn into an obsession.   Great advice already, if you can, identify the sound signature you are after.  It can vary depending on design.  Some designs lean into tube magic, bloom.  Other designs focus on bridging the gap between SS and Tube amplification often leading to Tube amps that sound more like SS amps with a touch of Tube magic.  If you are new to tubes if you can find a unit with auto bias / bad tub indicators it will ease you into the maintenance of keeping Tube amps running, sounding there best a bit easier. 

I think a PrimaLuna EVO 100 Integrated is a great starting point. 
 

Very good quality and built like a tank. It’s also easy to tube roll.

Vincent Audio has 2 models below $1000, look for B stock or open box. Not very tubey sound but that was just my ears, my speakers.

You could also get a preamp with tubes, my favorite pairing is tube preamp, SS amp.

@scotthiga   If you really want to experience what tubes are all about suggest you do a simple  SET integrated with a full range driver.

Check out Analogue Ethos.  You can do a kit or prebuilt. Beautiful cosmetics and I suspect great sounding as well. Other great options would be Erhard Audio, Elekit, AN kits, among others.   Pair that up with an Omega speaker (or similar efficient easy to drive design).

Certainly you could go with a push-pull tube design if you want something to drive your current speakers.  Just keep in mind not all speakers play well with tube amps. Synergy is key.  Otherwise, you could end up with something inferior to your current amp.  (BTW, it would be helpful if you post more info on your system. Otherwise, you will get many random opinions--including mine.)