An AR is a great gun, but you will shoot it alot. Most likely you will shoot different ammo through your bolt gun, even if caliber is same. This is due to mag length and rate of fire differences.
A DPMS 16" M4rgery for $1000 seems good to me. DPMS is a fine brand, but not a premium brand. "optics ready" is usually code for no sights. 16" is a good length. Long enough to be legal and accurate to 300 yds or so. Short enough to use for SD or HD.
223 vs 308.... I would go 223/5.56 everytime based on cost to buy and shoot. To me , a 308 AR is a specialty piece for a specific purpose like antelope hunting.
Just my 2 cents.