$300.00 dollars sounds a little lite. Are you looking at brand new pistols?
Every couple of months I shoot a 22 rimfire match with a group of other shooters at one of my gun clubs. They're very good with their 22 LR pistols, too! What has always stood out for me is the fact that these fellows take 22 rimfire matches very seriously; AND every single one of them (except me) uses one form, or another of either a Sturm-Ruger, or Volquartsen/Ruger 22 LR pistol. I guess these pistols start at somewhere around $600.00 dollars and go all the way up, 'into the stratosphere' after that. (There are $15/18 hundred dollar pistols on the firing line!) `
Now, you certainly don't need one of these outstanding rimfire pistols in order to target shoot with your boyfriend; the point is that you can't go wrong with a 22 LR pistol made by Sturm-Ruger. Here, my only suggestion would be to try to get one with a, 'bull barrel'. I would, also, suggest that you stay away from any pistol made by any company other than either Sturm-Ruger, or Browning. (Unless, of course, you want one of Smith & Wesson's high quality $1,500.00 22 LR pistols.)
In my opinion, THIS would be a perfect choice for you to make! The other way to go for a quality-built 22 rimfire pistol is, HERE. Either way you can't go wrong! (Suggest you also pick up, at least, one extra magazine - OK!)
Just so you know, this is one of the 22 LR pistols I regularly shoot. When I compete I use it with 5 extra magazines:
http://imageshack.us/a/img850/1757/k4wq.jpg (It's a Smith & Wesson Model 41.)