archerobx,
The .222 won't give you the range that the .223 does, which won't give you the range the .22-250 will. That said, it will probably still work well for 90% of the shots you'll get.
If you can get a good price on the Savage, your doin' a lot better than me. Those combo guns are sure demanding a high price nowadays.
As for fur friendly loads for the .223, I have been asking around and there doesn't a definitive answer. The opinions I've received are so varied, that I took to asking various bullet manufacturers. Traditional varmint rounds seem to be too explosive to use on coyotes, if you want the pelt. I also asked about match bullets and was told they also create too much damage. Ty Herring, from Barnes bullets, told me that his Varmintor bullets would also cause too much damage, so I should use his more traditional X bullets. I've looked around the local stores, Cabelas, and Gander Mountain, but haven't found them yet. I think I'll have to order some online to try.
Don