I'd go with the .223 If those were my only 2 choices. Like warpig stated is cheap, Find brass cheaper for reloadin and it's found anywhere. If me I'd go with a bolt because I'm more fond of the Bolts then the auto's. if ya looking for a good cheap gun to been used all around. ya can find Break over single shot rifles For well under $200. Plus with most of the single shots if ya get tired of that Cal. ya can buy a replacement barrel in a diff. cal. of pretty much any Cal. on the market. Most around here use the New England arms. But after I shoot there .223's I'm still glad I went ahead and bought my 22-250 But thats IMO.
The .222 was a pretty successful target cartridge, but the .223 can be very accurate as well. I don't think you could tell much between the two in the field or from a standard production rifle. The more standard CZ's in 223 or 222 sell for closer to $400 around here, and they are great rifles. I have shot a few 223 chambered CZ's and they were all incredibly good shooting rifles. In fact I think I will have to buy one for myself soon. As to which cartridge you choose, that is up to you. If your going to reload the cost would be pretty even especially after the initial purchase of the brass. However, the 223 is quite common and although I reload I like the idea of being able to pick up ammo anywhere. Both are fine cartridges.
Frosty, I have had the .222 Rem. and loved it. Of course I reloaded for it and it was great. then I found a S&W 1500 (made by howa) with a bull barrel in .223 topped with a Weaver T16 scope. This rifle will cloverleaf 5 shots at 100 yds all day long and never kick a bit. I would go with the .223. Just my .02 cents.
If I could find another Remington 788 in the .222 caliber I would pay the extra on getting the brass. When the military went to the .223 the gun makers saw a way to sell more guns. Let us face it that is what they are in the money to do. I feel, such as some bullet mfrgr's such as Sierra believe that the .222 is the most accurate 22 centerfire caliber out there. I will have to go with the 223 though since I can't find the 788.