As Mac said, it really depends on what you want and what $$ you want to spend. If you want a Bolt, then get a bolt. The Savages are great rifles out of the box and are an easy platform for rebarreling in the future.
If you want a Single shot, then the NEF/H&R's are excellent little rifles with the added versitility of interchangable barrels on the fly. Like all manufactures you will find some rifles that require more "attention" to get them shooting as desired than others. NEF/H&R puts out a LOT of rifles and if I'm not mistaken is the biggest manufacture of single shot rifles in the world, so your bound to get a few that need more "attention". And if it doesn't, then CS will take care of it...just be nice
Either way you won't go wrong, though the Handi is just so, well, Handi
After you get 1 then you realize just how much so. Short, compact, great caliber selection, relitively light, simple, rugged, the list goes on...
-Aaron