How important is a free floating barrel on a .223 being used for target shooting, prarie dog hunting, and coyotes? Also, how important is a heavy barrel compared to a medium or regular barrel?

Thanks Bryan

As usual, the answer is "it depends". I have a few older remingtons, that like the upward force on the barrel. They shoot subMOA. So I sure ain't going to monkey with them. But I have a few bolts that didn't shoot well with that forend pressure, so I grinded it out, and with the help on several on here, I freefloated and glass bedded them. And now they shoot better.

As far as heavy barrel is concerned, I find the heavy barrel has better cold bore performance and not as finicky when working up a handload.

I think most properly bedded rifles shoot better with a free floated barrel. If I had a factory rifle that shot well with bedded barrel, I wouldn't mess with it unless I was prepaired to redo the bedding.

Lot of different angles here. If you just absolutely can't get the gun to shoot sub-2-3'' with any factory ammo, then I would say you have a problem. If you are just hard certain it is not your scope and/or mounts, it may be the bedding. If you are not confident in your ability to check this, take it to a reliable 'smith for his opinion.
Lots of guns will really respond to handloading if reasonable groups are being obtained from factory ammo. It may take lots of trial and error attemps to find the "sweet load" your gun likes, but once that has been established, you will have the satisfaction of knowing that you have tailor-made the best ammo possible for your particular gun
I have guns that like the factory pressure points, and I also have guns that I have free-floated after some initial shooting decisions.
Free-floating, if done correctly, involves more than just removing the pressure point in the forearm. Firmly mouted actions, whether pillar bedded or solid bedded, the chamber area of the barrel solid bedded, plus the understanding of the recoil lug bedding are key components of a good bedding job, along with the floating of the barrel.
It is generally not a situation that is to be entered lightly. Try all possible alternatives before you try the bedding. I don't know what commercial gunsmiths want for a complete bedding job nowadays, but I'm sure if you get a pro job, it may or may not solve your priblems. A bad barrel is just plain a bad barrel.

I should have told the whole story. I have 2 Remington 700's. One is a 300 ultra mag, and one is a .270. I love them both. I just traded my AR15 in 223, because it was not my cup of tea. I'm looking for a good .223, without breaking the bank. I was all set to get the Remington SPS whenI noticed the barrel was not free floating. I've been looking at the Savage and the Remington. I was just wondering if the free floating Savage, which is cheaper, would be better than the Remington SPS without a free floating barrel.

I have remingtons that shoot better than most savages, and know my buddy on here Mossyoak33 who has savages that shoot awesome. Man, only way to tell is to shoot it and find out.

I would proabably opt for a savage if I was in the market for a 223 bolt.