Sureshot,
Good to see another GA member!
Personally, I would never recommend a .223 for deer. I know people have taken whitetails cleanly with a .223, but I feel you can only do this under the most perfect of conditions. Of course, most of us who've hunted know that perfect conditions rarely present themselves in the deer woods!
Now, before I get in to this, I have to admit I've never shot or hunted deer with the .223. However, I have hunted with a .243, and I would consider it the minimal cartridge for deer sized game. I've seen well constructed 100gr bullets not penetrate well in deer, and that leads me to conclude a 60gr .22 bullet would do even worse. I like to shoot all my deer through the shoulder, and I prefer to always have an exit hole. I just don't think a .223 can reliably penetrate two shoulders, and have my doubts about one shoulder. I understand if you plan on shooting behind the shoulder, but there are always times where we don't hit what we are aiming for. In those instances, I want to be assured the bullet can do the job.
If I had to choose a target/hunting rifle out of the current Handi selection, I would go with a .25-06. I know a few have had problems getting the .25-06 to shoot, but more than a few members have gotten excellent results. Mine averages around an inch, and I've only scratched the surface (and have tried very few loads with the gun, mainly loads that I had left over from other rifles). I know some may suggest the .308, but recoil can really work on your shoulder after a long day at the bench. With the .25-06, you can shoot 87gr bullets for target work, and step up to 115's for deer, and the recoil is very nice!
Or, you could simply a .223 and have whatever deer barrel you want to it!