I second the Contender, in 7-30 Waters or 30-30 to start. I just bought one myself, ostensibly to train youngsters, but I gotta admit, it is a nice little rifle for me, too.
Also, Thompson Center makes a youth length buttstock for the Contender, which you may find more comfortable, and if you grow (don't know your age), a full size stock will screw right on. Add to that the fact that you can get a .22 long rifle barrel and practice for a buck a box, and the Contender is hard to beat, unless you need to shoot beyond 200 yards or so.
If you hunt in the western prairie, where shots over 200 yards may be the norm, then I'd say go with the 7mm-08 or .308.
If a bolt action is what you want, as a lefty myself, I recommend Savage. They seem to have more to offer us than most other manufacturers, for a better price. My first rifle was a left hand Savage 110, and was an excellent rifle. The lefties come in 308, 7mm-08, 243 (in the short actions), plus several long action choices.
Most important is get something you will be comfortable shooting, and can afford to shoot somewhat often. Beyond that, there are lots of great deer rifles/cartridges. For my money, the good old 30-30 is about ideal for a new hunter ( or old hunter who is tired of getting the snot kicked out of him by his Magnum, i.e. Me), who probably shouldn't be taking 300-plus yard shots at deer anyway (neither should I). It's plenty powerful, ammo is cheap, and it comes in handy, economical rifles that are generally an excellent value.
Good luck, and enjoy our sport.