First deer rifle. Not sure if you already hava cliber in mind, but there are a buinch of good ones out there. Everybody ight tell you something different, but I am sure that it will most likely come down to .243, .270, .308 or maybe 30.06. Just a matter of preference. All will kill dear effectivly. You will get better input from some of these other guys on caliber.
As for the left handed thing I really understand that, beter than most. I am a left handed shooter as well. Actually, I shoot both, extreamly well, though I have gotten to where I prefer to shoot lefty. My suggestion would be to get a right handed Bolt Action. This comes from experience as an Army Sniper. If you are shooting deer, or anything else, and you are shooting form some sort of rest... ie, ..... a branch, a bibod, a backback, whatever, as a left hadned shooter, and a right handed bolt, you will never have to take your hand off the trigger for that follow up shotshould you ever need it. you can stay right on stock with your cheek, cycle the bolt with your right (non-firing hand) keeping your finger on the trigger for that fast follow up. getting back on i\target , or keeping the target in the crosshair is harder to do, if you have to come off the stock to cycle the bolt. This might not work for you, but, it does, work better for me. Give it a try, and think about it. Might take a day at the range to get used to.
Depending on the rifle, if you go with a semi, you might be OK. Just depends on how it ejects the brass.


Hope this helps, and good luck.