Probably the "best" sub 200 dollar guns I can think of:
Pistols- High Point (I may get some flack for this but) I have one and love the thing for what it is.
Phoenix Arms HP22- the only .22 auto, that will cycle ANY ammo, it just doesn't have last round hold open, but the manufacturer sells a kit to convert it.
SCCY CPX2 got mine from CTD for 204, well and 11.00 shipping and a 15.00 FFL transfer fee, so just a TAD over your limit, but still a GREAT deal non the less
Rifles- Mossberg 702 plinkster is a pretty good .22 for the money,
Savage Bolt action and semi auto .22's, Marlin .22's, and of course the 10-22
AND the BEST CHEAP RIFLE ON THE PLANET THE MOSIN NAGANT they simply CAN NOT be BEAT for 100 bucks