What YOU can see through any scope only you know. Go where you can check them out. Look thu them. This requires being able to look thru them outside of the store. Hard to do at a lot of places. A good place is at a range if someone will be kind enough to let you look thru theirs. A 9X generaly enough for hunting out to 500.
Having stated you want more, your options are endless..12X to 80X. And here is where the budget comes in. What do you want to see at 500 ? A variable is more suitable for hunting. I would imagine not all shots will be at that range and an animal encountered at say 200 would be more or less out of the question with a fixed power adjusted to longer range. Tactical scopes are a good choice being they have a wider range of adjustments than traditional scopes for elevation and windage, up to three times the clicks. Maybe I'm preaching to the choir here but at ranges over 300 being able to see mirage is a benefit. To some who dont know how to use it an annoyance.
Types of crosshairs will be a benifit also. One with a Miladram ranging system (Mil-Dot) is useful.
Quality of Glass = $$$. Leopold, Nikon = Good, Zeiss, Nightforce = Real Good, March = And many, many more.
I, and I dont think anyone can tell you exactly what to get. Check a lot of them out and weigh all options. Let us know what you come up with.
As SWO1 said a 9x is enough to shoot out to 500yds. Too much magnification becomes hard to hold steady under field conditions. Quality...clarity and brightness...are more important when hunting than super high magnification. For a hunting rifle I would not go higher than 4-12x44mm.
It is hard to find a variable power scope that the image is equally good through the entire power (magnification) range. This is where quality comes into play. It is better to buy a good quality 3-9x than an average 4-12x and find out it is not useful past 10x anyway. JMHO