I don't know if HLSL is up to date enough for 4K, I would assume it is but not sure (edit: apparently it is). It's a lot of pixels though so you better have a good GPU for that, like not a decade-old 1gb antique.
32" 4K VA FreeSync are available, LG 32UD59, Samsung U32J590UQ, BenQ EW3270U, etc, browse and you'll find more.
IMHO the ideal for you would be a WQHD (2560x1440) VA w/ FreeSync then, but they're a rare breed, the Q3279VWF is the only recommendable one but now EOL w/ low stock, otherwise there's the more expensive pc-gaming-oriented LG 32GK650F.
Most other VA choices at that resolution are curved.
Don't bother looking around forever for the ideal 1440p if the 4K are more easily available though.
Note: do not mistake the Q3279VWF (VA) with the Q3279VWF8 (IPS)
Note: the range, most emulated games in MAME are between 50Hz and 60Hz so a 40~60Hz range would be fitting, though there are some slightly above 60Hz that won't be handled by FreeSync...if you want to be sure all games are then pick one with a broader range, some FreeSycns are like 40~75.