I'm fairly sure the Remington 783 and Marlin XS7/XL7 are almost the same rifle. Maybe even built in the same factory?
I have shot a friends Ruger American and it feels just as cheap as the Remington or Marlin and was not any more accurate. But they are usually a tad more expensive.
For the most part, most of the cheap rifles will be MOA or close to it out of the box anymore. The manufacturers have figured out how to make accurate rifles cheap.
Even though I have a couple Remington 783's, that would not be my suggestion to you if you know that you want a new barrel immediately. Just purchase a Remington 700 action or Savage action. Not rifle, just the action. I have no regrets with my 783's. I have learned a ton by not being afraid to modify them and I am still trying things and using them to learn on.
Although if I wanted a 458 SOCOM on the cheap I would probably buy a Del-Ton Lite AR 15 to re-barrel. Those can be found for just a bit over $400 new. The 458 SOCOM was created for the AR platform.
Some of these "cheap" rifles that have been suggested are still $1,000 guns. That's not really a fair comparison when you can still get the 783's closer to $200 after the Remington rebate.
Whatever you decide, just know that there really isn't anything as a budget build. You always end up sticking more money into these projects than originally planned.
People will say things like, "Why would you put money into a throw away rifle like the Ruger American/Savage Axis/Rem 783?"
Oh crap.... wait... isn't the Ruger Precision Rifle that everyone has a hard on for just a Ruger American rifle in a chassis stock? Yeah, pretty much. At the very least I know it is the same action. And people are spending over $1,000 on those every single day.
If you really want to do a 458 SOCOM in a bolt action, you'll probably be best served starting with a Savage action and building from there.