Welcome to Predator Masters, Cameron. Just jump right in and hang on.
As to a left-handed rifle, I don't know about that one, but you have already been given some good examples from others. As to the usefulness of rimfires, I do have some knowledge about that and will share them with you.
As to the caliber you choose, it depends on where (distances) and how you will hunt. A rimfire is fine for groundhogs / rockchucks, and crows and a variety of other small game or varmints if the range isn't too far, and if your aim is true. The .17 HMR is a fine crow-sniping round, flat shooting and accurate. Eastern groundhogs will drop to either the .22 magnum or the .17 HMR, as they will to a .22 long rifle. Probably most of us "old guys" started out with a simple .22 rifle and have taken a good variety of small game and varmints with them.
Years ago when I was in the Navy, stationed in Norfolk, a farmer in the Chesapeake area told me that the locals controlled the exploding deer herd at night (definitely not legal, bordering on sinful) with the use of 22 long rifles. They weren't poachers for the fun of it, but rather farmers that were fed up with the crop damage they were having. Their soybean fields were being destroyed. Not that it mattered since it all was illegal, but they gave the meat to local people so as to not waste it. The noise level was low, which was good in a relatively populated farming area, and the cartridge worked with proper bullet placement, dropping head-shot deer with regularity. Please note that I do not advocate the use of a 22 long rifle for deer. Never have, never will. I'm only pointing out that it's more of a cartridge than it's minature size indicates. We all have much better rifles suitable for deer than that, but the story is worth telling because it illustrates the power / usefulness of the little .22 round. For small game and varmints, it's a great cartridge.
Before any of you decide to begin an all-out assault of me for telling the story, go back and read it thoroughly before casting stones.
After many years of shooting a 22 rifle as a boy, I graduated up to centerfires for groundhogs. Still, I cherish those days gone by, with my .22 in hand, out in the fields and woods hunting the "big-game in my area," groundhogs and fox. I hope you are able to experience the same great times, Cameron, that I and most of us on here have.
Just remember to practice with your rifle / load combination, take your time on the shot, place the bullet where it needs to go, and let the fun begin.
Oh, and we like pictures, so don't be shy.
