Hello and welcome!
I'm assuming that you mean that you only have $1500 to spend on Rifle scope combo and I will focus on factory rifles rather than costom. You can have a custom built for 1500 easily, but I'll let someone more knowedgeabe fill you in there.
There are litterally hundreds of options. If you intend to be limited to 500 yards and want to use it in the brush and field then you will want a sporter weight rifle or a mountain rifle. You will not want to lug a Sendero through the thickets. Many will steer you towards a Savage, but not me. I am a Tikka T3 fan because the shoot straight and they are inexpensive. Other options would include a Remington 700, Howa 1500, Win 70, Browning Abolt. Sako are excellent, but getting out of your price range.
Do you reload?? If you don't than you will want to stick to something that is fairly common so you can get rounds for it. 260, 270, 280, 308, 3006, 7mm rem, 300 WM.... the list goes on. Shot placement is key, so you can take deer sized game at long range even with a 243, but I favor a little more power. I shoot a 300wsm and I can see now that I could have gone with a little smaller round, but I like the added knockdown. If you will hunt in brush most of the time, then stick to the heavier rounds from 3006 and up. My next build for long range deer is going to be a plain old 260 rem.
The thing is it is always a give and take. If you want a really flat shooting rifle that will give you a little more leeway in your range estimation you will pay for it in barrel life, cost of bullets and recoil. Don't let anyone tell you to get a big mag so you don't have to aim much higher to tag one at 500 yards. Even a 270 AM will drop some at 500 yards. Get a rifle you feel comfortable shooting and won't wreck your shoulder
Spend money on you glass!!! minimum of 400 dollars in my opinion and if you can afford it, and plan on dialing your shots at great distance, you will want to look at spending more.
good luck and fill us in on more information of you prefferences.