The TPA3250 is a stereo amp, where the LM3886 is mono, so you would need two LM3886 for the powered monitor. Lots of heatsink on the cabinet back for the LM3886's.
The TPA3255 is a lot higher power, 315W max stereo, so really overkill for the minimonitor.
Both the TPA3250 and LM3886 can be used with balanced inputs for studio use without problems. I used the older LM3875 with balanced inputs with very good results. The only thing might be startup transients, so probably a turn on output relay maybe needed for the LM3886.
Just make sure you are getting real IC's. Had some Ebay LM3875's that were giving startup transients where the ones from Digikey were fine. And I built at least 12 channels worth and those were the only two IC's that did have transients.
Sounds like a fun project to me either way.