Is there a particular reason you're dead-set on .243?
If you want something as AR-15ish as possible, why not just get an AR-15 in 6.8 SPC (.27 calibre)?
If you want "powerful enough for deer, without too much kick", the 6.8 SPC appears to be popular for that. Maybe you can go read up online and see if it meets the game types and hunting conditions you expect to face.
If 6.8 works for you, you're in luck. It's probably the second-most common centrefire AR calibre these days, and a new 6.8 upper receiver isn't any pricier than a usual .223 version. You can save a lot of money by buying an AR-15 "stripped lower receiver" (still legally a firearm and will have to be bought by your parent), installing a "lower receiver parts kit", and then putting a new 6.8 upper on top of that.
By building your own lower, you could save several hundred dollars over the cost of buying a complete gun. Building a lower takes minimal tools, very little time, and basically no special skills beyond reading instructions.
A basic breakdown:
-Quality lower receiver, maybe $150 on a good day
-Good lower parts kit, $65
-Used stock assembly, maybe $30
-Good quality Rock River Arms complete 6.8 SPC upper, like so $540
So that's looking about $800, give or take a little and maybe some shipping (but at least no sales tax). Then just toss on some sort of optic, or get some used iron sights from an online forum. And that'd be a heck of a good rifle. Just make sure you get magazines that are limited to a capacity allowed for hunting in your area.
Is this the kind of thing you're looking for? I can't think of much reason to be absolutely stuck on .243 unless you just have cases and cases of it stockpiled in the closet. 6.8 fulfills a similar role, and is becoming more and more available every year.