If you can find them, I would go with the Burris Signature rings on the base you have. You can use the offsets to get additional elevation, if needed. With a good scope, you may not need any. Without knowing your financial limit, I would recomend a Vortex Viper or Nikon Buckmaster. I have three BMs, two mil-dots and one duplex. They are easy to use, good optics, and the turrets work good. I found all of mine used for $225 or under.
The Vortex is very hard to beat. Great optics, great warranty, good selection. Priced from $279 for a 20x variable to $1000+ for a first focal plane.
One good thing about optics, you get what you pay for.
I assume you are shooting a 243 or 308 in that 788. Your base is good for what you can do for now. Later, when you are more experienced, you will know what you want in a different rifle. Oh, you WILL want a new rifle.