Both the Remington 700 and Savage are exceptional actions, both have an abundance of aftermarket parts, and both will build exceptionally accurate rifles. So you really can't go wrong either way in terms of choosing between those two actions, and if you ask around you'll find plenty of people with nothing but good things to say about both of them.
As far as accurate range of the 223, with heavier bullets the 223 is a quite capable 600 yard rifle as evidenced by the 1000's of shooters that use iron sighted AR's in High-Power Service Rifle Matches. The 1:14 barrel is far too slow a twist to stabilize anything but small, varmint bullets. Optimally a 223 barrel for those distances would be a 1:8 or 1:7 twist to stabilize the heavier bullets, although 1:9 will still do quite well with a variety of loads and many guys who measure their 1:9 twists find that they're actually a little faster. Still, with 1:9 barrels in a variety of rifles I've had good results with the Hornady 68 BTHP, the Sierra 69 MatchKing, and the Hornady 75 BTHP. Each of these have relatively high BC's for the caliber, and will do well to at least 600 yards. The Sierra 69 MatchKing is a favorite for high-power shooters, and has been an exceptionally accurate round out of most everything I've ever shot.
Optics and stocks are both really matters of personal choice and intended application. I'd say the best thing to do is handle several different styles of stocks on various rifles before you settle on anything. The nice thing is that aftermarket stocks for both rifles are readily available at all different price points depending on what you want to spend. Scopes too will require some additional research, and will depend largely on your budget. A 223 isn't going to be too awful hard on optics, which means you might be able to get away with some of the more budget priced optics more than on something of a larger caliber. Still, the place where a good optic is really going to shine is in repeatedly returning to zero and maintaining good calibration as you dial up windage and elevation adjustments on the range.
The Savage Stevens and BSA optic you mentioned at $299 isn't a bad deal, but it's not necessarily stellar either. $300 is about the going price for a new Stevens 200, and the BSA Sweet 223 is about a $60-70 optic. The BSA Sweet 223 you mentioned will get you out shooting on the range, but it's not anything you'd want to keep long term if distance is going to be your objective. So if it's in good shape and you could sell if for $40-50 then $250-260 for the used rifle is not bad at all.
So there are some thoughts for consideration. Hope that helps push you a little further in the research and decision making process.