I've had a lot better luck with Simmons than most people online seem to, as have most of my friends. So I'd not be afraid to try it out with that and if it works, use it until I could afford to upgrade. I've got a couple of friends that use them on 30-06's and the ones they are using have held up just fine.
That said for a scope under $250, I've used many of the options in that price range and my favorite by far is the Burris FFII.
That said for a 4-500 yard shot, it has a lot to do with the shooter, and there are two ways to get there. The first is hold over, and you can practice with one of the holdover reticles like the ballistic plex in the FFII, or the Nikon BDC reticle and you can probably get good enough to get hit's on a decent sized target. I'm not a fan of this method, and they don't calculate for wind, or anything else, so you still have to worry about that. So it's not just putting the dot on target and shooting. IMO these reticles instill a false confidence in many people, and give them the confidence to take shots they really shouldn't be taking. I'm not a fan of that, nor am I really a fan of these reticles, and to me they often cover up enough of the target, or in Nikons case the circles are large enough that you can't be but so accurate with them.
The next way is to use the turrets to adjust to get there. This is my preferred way, and a lot more fun imo. The problem is a lot of the cheaper scopes don't track accurately enough, and aren't repeatable. The SWFA SS are one of the budget scopes that are pretty decent, but you are looking at $300 for a fixed power scope, and they go up from there. The 3-9x42 variable power scope is $600, so they are all out of your price range. You can get a fixed Bushnell Elite 3200 10x in your price range, but having had one, I wouldn't want it nor a fixed power SWFA SS on a hunting rifle. IMO the best option here would probably be the Burris FFII and when you can afford it, have Burris add their tactical turrets for $80. I think this is about as good as you can do for the price, and would give you a great hunting scope, and something you can play around with, and should get you out to 500 yards.