Lots of very well-informed advice by others already, but I'll throw in mine as well on the possibility it will benefit you.
I am a late-comer and convert to the AR game; I am from an era when "serious" rifles had calibers that began with the number "3" as in .308, 30-06, 300WM, etc. However, even old dogs - and I am an old dog - can learn new tricks, and once I took a hard look at why the AR platform was so popular, I changed my mind. They are versatile, can be customized in just about any preference, and also are comfortable to use and ergonomically very well set-up. They are also, for a gas gun, relatively easy to learn to take down, clean, lubricate and reassemble. If you get an AR chambered to shoot both 5.56x45mm NATO and .223 Remington, you have two potential sources of loads. I favor a 1:9 (or 1:8) twist rate as the best compromise between stabilizing light bullets and heavy ones - but your mileage may vary. Many folks who use ARs train and practice with 55-grain FMJ, while reserving lighter calibers for varminting and heavier loads for longer-range shots.
A 16" barrel M4 carbine type of AR will be suitable at 100 yards (indeed well past that) but if you want to have the option of reaching out further, you might want to explore an 18 or 20" barrel - the latter being the government-issue or traditional AR-15/M-16 design. If you really want to get ambitious, and have the money, Rock River and some other manufacturers make match-grade rifles in 5.56/.223. A qualified gunsmith can also make one for you, or you could even do it yourself. Lots of folks these days build their own ARs.
My favorite value for the money is a Windham Weapons SRC - which is an extremely well-made carbine with a 16" barrel and 1:9 RH twist barrel capable of handling anything from 50-grain loads up to 69 or even 77-grain slugs. The local Cabela's has them on special now for $850 plus tax - which is a very good deal.
Be advised that semi-automatic gas guns are harder on brass, so if you reload - you can't count on as many uses for the cartridge cases as you would be able to do with a bolt-action. Personally, I use 5.56/.223 cases three times in a gas gun before recycling them, whereas I can get 8-10 uses from the same case in a bolt-action. Something to think about if you plan to load your own ammunition. Invest in some training on how to reload before attempting it yourself; the NRA offers a great workshop. Lots that can go wrong if you don't know the pitfalls - but it can be very rewarding once you know how to do it properly.
Far as a bolt-action rifle in .223, they've loads of fun, easy on your shoulder, and usually quite accurate. You can get a very good Savage or Ruger .223 for under $800. Some manufacturers are now offering competitively-priced rifle + scope combos, too.
Many shooters enjoy and use rifles chambered in .223 because they are cheaper to "feed," around $0.40-0.50/shot for most factory ammo, versus around a buck a shot for .30 caliber rifle ammunition. That's something to consider in today's commercial environment. If you opt for 22 rimfire (22LR for example), it is worth nothing that rimfire can't be reloaded using commonly-available commercial reloading equipment. .22 caliber long rifle is great fun as a plinking round out to ~ 200 yards, but runs out of gas after that pretty quickly, whereas the .223 Remington/5.56mm NATO can reach out to 600 yards + in the right hands.
Bolt-action rifles are mechanically simpler than semi-automatics - and are generally of more robust construction. The former are easier to clean and maintain and are also easier to get tight groups out of than semi-autos, in my view - although there are certainly people who do amazing things with ARs these days in matches and the like.
Don't know if you are interesting in hunting or not, but most states allow varmint and small predator (such as coyotes) hunting with the .223 round, but not all allow deer hunting with it.
Good luck - enjoy your new purchase...