For your budget...I would recommend you go handle several versions of the following rifle...the fit and comfort of the rifle is just as important as any other quality. All these rifles should be able to be had for $500 or less if you shop around.
- Tikka T-3 lite (great triggers, excellent accuracy and handles nicely)
- Savage 10/110 with accu trigger (good trigger, excellent accuracy and a sold gun)
- Remington 700 ADL (OK trigger, very accurate,solid gun)
- Browning x-Bolt (nice trigger, good accuracy, ok wood stocks)
I have all of the above rifles in one form or another and they all preform very well. The Tikka is my favorite hands down right now. The Browning may be hard to find in your price range.
Scope options...you should be able to locate any of the below in your price range...there are several other options as well...these just represent a few of my fav's...
- Nikon (Prostaff, Buckmaster or Monarch) are all good and if you shop you can find them in your price range...I love my Nikons!
- Bushnell Elite (I have an Elite 3200 and really like it)
- Burris
- Redfield
- Swift (I love them...but they aren't easy to find...awesome eye relief and rock solid reliability)
Look through the scopes and find one that has the eye relief that work for you...some vary greatly.
Invest in good rings (Millet, Redfields, Burris, etc)...well worth it.
Caliber...I would recommend any of the following calibers for you based on what you said and based on ammo availability and cost.... .243, 25-06, 7mm-08, .270, .308...leaning heavily toward the .270 and .308 for versatility (due to large selections of various ammo and bullet weights)
Good luck and take time to find the one that fits you best! Handle plenty!