Recently purchased a Remington 700 SPS Stainless .300 RUM with 26" barrel. Changed the stock already to a laminate thumbhole. I have never tried to shoot more then 200 yards so I am very new to long range shooting. I shoot a really good group at 100-200 and really would like to learn to shoot to about 500-600 and maybe even further if possible. I will be hunting deer with this gun. I know it takes a lot of practice but I was wondering what would be the best optics, rings, and bullet for this gun? I am interested in the scopes with turrets because it seems to take the guess work out. Not big on the mildot scopes I usually like my crosshairs fine. I would like to spend around $1000 or less for the scope but will considering spending a little more. This is a hunting rifle so I would like something that is very good in low light as well. Thanks for your opinions in advance!
Sounds like you are off to a good start.
As for scopes, with that budget you have a long list of options.
I'd say stick with the 50-56mm objective lenses and minimum 14-20x magnification.
I really like the Zeiss Conquest, Leupold VXIII, VX7 and Mark 4 tacticals, all of which you can find within your price range in the above powers and objectives.
Don't be afraid to check the classifide ads here, Sniper's Hide, or even on ebay for used scopes as both Leupold and Zeiss have Lifetime warranties.
I'll add one more too, and that's to go with the 30mm tube as it will give you a wider field of view and more MOA adjustment typically than the 1" but, 1" will work as well for most applications within 1000yds. The Zeiss Conquest series with the z-1000 reticle would be one that is great to start with.
Pesonally I do like the mil dot scopes because they give you a good set of reference points to use to see how far you are off when you are not using a good spotter. That'll really help with adjustments.
Till you get yourself a sufficient quantity of brass saved up I'd say go with factory ammo or from a custom loader like Conley Precision Ammunition.
Get out and shoot as often as you can, make notes as to wind, temp, humidity, and how well you shot, and you'll then start building a comparative database.
Welcome, good luck, have fun, and don't be afraid to ask questions. There are a lot of people here with a great deal of expertise and most are pretty nice guys.