The .17 is cheap to shoot. A little more accurate and longer range then a standard .22.
5.56mm ammo is no longer cheap. It is running $450-500 or more for a case of 1000 rnds. That being said a decent AR-15 will run you about $750 unless you build it yourself. Cheap optics will run you another $100. Decent optics will ocst $300-400 or you can just use the iron sights. I had a very nice AR built for me with a free floating barrel that is positively one of the most accurate rifles I own and it only has a 16" barrel (1 in 8 twist). It ran about $1100 with all the things I wanted on it.
If you really enjoy target shooting go with the Savage. I have a Savage 10FP with the accu trigger. It cost me $508 stock. I put a decent scope on it that costs about the same but you can put a cheaper one on to start. The .308 cal. is accurate and many factory loads are available that will duplicate all but the very best handloads. Mine shoots sub moa groups out to 300 yds. with Federal Match ammo. The reason I like this rifle is that I own other rifles made by Weatherby and Remington that shoot about the same but cost twice as much. A little out of your price range but worth it. As you can tell I am a big Savage fan.
I don’t like the AK rifles. I know many do. Yes they are reliable but they are not generally accurate until you put a few mods into them, which makes them less reliable. That being said I own one but I don’t think they are the bargain they once were. Good for 50-100 yds. Maybe combat accurate a little further out but I just shoot at targets these days so I like to hit a little tighter then they are capable.
Always nice to see a good gun thread on T-Nation.