OK, here it goes......need help for new Savage!!

[big honkin jeep]

Just by your description it sounds to me like you're just looking for an accurate, economical plinker.
Super accurate, contrary to popular internet lore, doesn't have to weigh 12# and have a truck axle for a barrel.
In my opinion the best way to "buy accuracy, especially for someone starting out, is to shoot a lot of ammo.
Most any modern rifle produced today is capable of sub minute accuracy with a load it likes.
As far as choosing a caliber, from what you describe I'd go with a .223 for a couple of reasons.
For one recoil is really mild and the cartridge is really efficient, fast, and flat shooting. Another good reason is bulk pack of Federal 55gr 100 round boxes are available at most "Big blue walled" stores for about $37. It will get you out a couple of hundred (400+) yards which may not be as far as a bunch of the "internet commandos" shoot (sarcasm) but is in reality a pretty far piece.
From what I've seen of ammo prices if you buy the cheap stuff ($19 per box of 20 )and catch it on sale, you may get 40 rounds of .243 at that price in my neck of the woods.
Just personal preference, but I prefer rifles based on the model 10/110 action (includes 11,12,14,16 and 110,111,112,114,116) to the Axis series of rifles
If you want something light and portable that you can walk around the woods with, any of the model 11s should do just fine.
If you want something a little heavier and or longer that you would be mostly shooting from a bench, then one of the model 12 "varmint rifles" (like the 12BVSS) is really nice.
Kind of a shorter, more portable but still fairly heavy option (due to the heavy but typically shorter barrels) that benches well would be one of the model 10 law enforcement rifles.
Not really sure what your budget is, A lot of guys here from all walks of life and one guys idea of budget friendly, may not be on the same planet as another fellas idea of budget friendly. Most of the rifles produced today, especially full featured Savages, don't need all the tinkering and aftermarket parts they did in years past to shoot exceptionally well.
Buy good name brand rings and bases and a good name brand scope. (Leupold and Burris make some affordable serviceable stuff) I cant stress enough that a good name brand mounts and glass is much more important than high magnification long sunshades and "tactical" appearance and will serve you better in the long run.

Good luck.