On one hand you have got cheap,plentiful and reliable and decent on fur (17 rem being best) on the other you have new, sexy and fast and maybe easier on fur (jury is out but new bullets are coming out) . 22-250 like trajectory on 223 cost (if you reload).
Since you added the criteria of handi the nod goes to the 204, it seems that there has been a change to the ejector system supposedly it is an extractor (the 204 was the first to come out with it). Again it's early in the game to see if stuck cases ( a common handi ailment but not un-fixable) are eliminated, but it looks good. It is unlikely there are 223's yet with the new extractor but the could start showing up. There is a thread in the handi forum on how to tell.
Just so you know I have a 204 on lay away and I own one in 243. The smaller bore rifles tend to be easier to get to shoot good. I don't know your experience with the handi but the folks at the forum can help out. They can be a little temperamental.
If you go 223 the white box winchester 45 gr loads seem to be universally above average out of a handi.
Don't forget the 22 hornet it's a good round where there are neighbors, and still has 150 - 175 yards in it.
