Your room size is similar to mine (13 x 17). I use JansZen Valentina hybrid ESLs paired with twin Rythmik 12G subwoofers. The JansZen’s are flat to 30Hz and do bass really well. With the subs I have the scale and impact of a much larger and expensive speaker. The speaker/sub combo fits your budget. I ran the JansZens without subs for a number of years, quite happy. The subs are a recent addition, icing on the cake.
The JansZens are an easy load for an amp so either SS or tube electronics work. Some JansZen customers I know (including me) use tube gear. We think that makes them sound the best.