I do like the LCR and I am a tried and true S&W guy. With a revolver the trigger is a good part of the whole thing and I rate the LCR as nearly as good as the S&W 617
Not a huge fan of the sr22 ,look around and buy a ruger standard model . Fairly compact and a really reliable gun that will pretty much shoot any high velocity 22 ammo out there and likely will also function with CCI std if you want something less.
The Standard model has the shorter barrel and fixed sights that are frowned on by many but I think just as good as adjustable on a 22 and less likely to get knocked around. The used Standard model should only run you $250 or $275 which will allow you plenty for ammo and allow you to start saving for a nice S&W 617 because what you really need is to get both!