Personally I would either go with the 10-22 or the Henry as a first gun. Second one would be the one you didn't get as the first one!
If you like the AR platform then I would suggest you save up and buy an AR. That having been said having a rimfire AR style is a great idea. Wish I had one myself. I am seriously considering a new rimfire that is being made by Franklin Armor, the F17L which is a Winchester Super Magnum .17 caliber gas operated AR style rifle.