If your kids can handle a 12 gauge, I would suggest a .270. Break them in on 100 grain bullets then move up to 130's when hunting. Savage makes a decent rifle for around $300. If you can find one used I'd stay away from wood; they tend to kick a little harder. From my experience a .243 will result in cripples. I don't have experience with 7mm 08, but I'd stay away from the 7mm mag. I've heard that the 25 06 is a good alternative to the .243. I've seen it kill plenty of deer, but it may be out of your price range in this area. Just my two cents. Hope it helps.
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