Re: $500 budget scope
You didn't mention what features you wanted so I won't be able to narrow it down much. I would suggest figuring that out before you start your search.
#1 Be sure to check the used section of this site and others. You can find some great deals at times on some higher end scopes that may fit your needs.
But even buying new there are a surprising amount of jewels in this price range, especially if you are willing to go with a 2-10, 3-9, 4-12, and 4-16 power range scopes. And IMO you should be ok with this as you don't need much magnification to shoot out to 700 yards on deer and elk sized game.
Zeiss makes a nice 3-9x40 in a plex reticle for under your price range. I think you could upgrade to the target turrets as well or get custom ones and still be under $500
Bushnell Elite has many good options under $500. You can even get into some of their custom reticles if that is a feature you want. I believe you can get the 4-16x50 for right at $500. I personally wouldn't go over 4-4.5x on the low end for a hunting scope so the 4x scopes like this are a really nice fit for low and high end magnification. Bushnell Tactical does have 2 that would fit as well, their 5-15 and the 10x. Both proven scopes and have nice features for the price, ie target turrets, mildot reticles, etc. Their rain-guard is a nice feature for hunting IMO and their glass is very good.
Weaver is one of my favorite brands for this price range. They make very durable scopes that have excellent glass for the price and their turret repeatability is as good as it gets in my experience. Look at the Grand Slam, Super Slam, and even the V series. The V16 is a nice little scope with semi target turrets and even has a custom reticle option now. I have 3 of these and have used them to death with no ill effects.
Hawke is a somewhat unknown name here in the states but they make very durable optics and their glass is coming along as well. They give you a lot of options for the dollar. Look at the Sidewinder, Sidewinder Tactical, and Endurance line. They are tough as nails and have a big following in the precision airgun and FT world which is a very demanding sport. I would buy new if you go this route as some of the older models didn't as good of glass as the new ones do.
Sightron SII and BigSky also have good options.
And Meopta and Minox have new lines that fit as well. Nikon makes some scopes that will fit too but I don't have as much experience with these 3.