Start cheap or money to blow?
S&W is good choice, Ruger auto .22’s are great pieces but are a challenge for a beginner for in depth field strip cleaning. Ruger . 22 revolvers are great choice but expensive. You might consider Rough Rider .22 revolvers they are decent.
Before moving to next level go to a range and rent various pistols and caliber choices. If you have a friend with several that’s even better.
Above all learn the Four Rules of firearm usage/safety, drill them into your head. Good hunting!