I'd also check out the Browning. I have a Browning BAR in 30-06 and I really like it. Has a awesome feel to it. At least to me. Accuracy could be better however, as long as you shoot Federal Fusion shells you can get really good groups with it. It took me a while to find that as some shells don't want to group together. It doesn't seem to jam infact I've never had it jam on me I don't think. One time it messed up but I wouldn't really say it jammed and I've shot quite a few hundred rounds through it. It's not picky about jamming but it's picky about shells when it comes to accuracy. All of them are close enough for a deer or something like that but the Fusions were the only ones I found that I was happy with. I love how the gun feels though. I've been told that the semi auto's often aren't as accurate as a bolt action anyway. I'm not sure if that's true or not but this thing is accurate enough for me once I found the shells it liked. I got mine at a local gun shop used. It was made in 1990. They make new ones though. The place was asking $550 for it and $223 for the scope and I ended up with all of it out the door with tax for $750 so I'm not sure what they took the money off of but that's quite a bit under your budget. Even with the new BAR's you could get one in your price range with a decent scope.

I'd check out the bolt actions as mentioned above too. I'm just a semi auto guy myself though.