Start by deciding how much money you want to spend. A BNIB Savage .223 can cost you as little as $600ish with iron sights. A .22 rimfire can be $300ish. $700ish for a Savage Package(Comes with a decent scope.) rifle.
Don't discount buying a used rifle either. Takes a lot of abuse to damage a modern rifle.
"...shoot Left Handed..." Doesn't really matter. Even with a semi-auto, shooting left with a right handed rifle isn't a problem. Been doing it for eons myself. (SMG's, LMG's plus a swarm of assorted battle rifles didn't matter either.) Empties get thrown a long way and rarely anywhere near the shooter. Never mind his face. And if an empty gets down your shirt, it doesn't make the slightest difference which side it came out. You're going to do the dance.
"...advantages of one over the other..." Other than cost, a .223, where legal, will let you hunt deer and varmints with a change of bullet, should you ever decide you want to hunt. A .22 is small game only.
Don't discount buying a used rifle either. Takes a lot of abuse to damage a modern rifle.
"...shoot Left Handed..." Doesn't really matter. Even with a semi-auto, shooting left with a right handed rifle isn't a problem. Been doing it for eons myself. (SMG's, LMG's plus a swarm of assorted battle rifles didn't matter either.) Empties get thrown a long way and rarely anywhere near the shooter. Never mind his face. And if an empty gets down your shirt, it doesn't make the slightest difference which side it came out. You're going to do the dance.
"...advantages of one over the other..." Other than cost, a .223, where legal, will let you hunt deer and varmints with a change of bullet, should you ever decide you want to hunt. A .22 is small game only.