I posted a similar answer a while ago... here is a copy of it...
What I believe, take it for what it's worth.
First I don't know what game you are in so...
Tactical... Go strong and heavy
Benchrest... Go strong yet light
Hunting Varmints... Go Strong, Go Heavy, Go Light, Go whatever you want
Dangerous Game... Go Express Open Sights
Going to a collectors show... Go for Looks, engraving and Gold is nice too.
Anyway...
For Benchrest we have the oportunity to use light Kelbly rings on their rail, or Davidson bases on various other actions. Or if you are using another custom action, the builder usually has rings to match that are strong yet light example would be BAT.
For Tactical there is only one way "Picatinny", not to be confused with "similar to Picatinny". The government has a set of .pdf drawings that have the exact dimensions and tollerances of a "Picatinny" Rail, it's slots depth, the rails width, the slots width, the slots spacing, etc. There are a few suppliers that have their bases and rings that meet U.S. Government specs on Picatinny rails. Glen Seekins of Seekins Precision is one. His Bases, and Rings are by far the best I have used. A scope that is mounted in that type of set-up, is in the best fixture possible. I would suggest single piece bases because they are one piece and provided that they are bedded and mounted properly, you aren't mounting your scope in a bind. The Weaver (cross slot) rings in my opinion are a cheap knock off of a Picatinny system. With the Picatinny System you can remove the scope by removing the rings from the base, then return the scope to the rifle in the same slot and be VERY close to where you were sighted in before (very was bold for a reason). I like the Leupold brand of Picatinny Ring as well, it is the Mark 4 series. I like a Steel Base, but I like Aluminum rings because they can bend and conform to the scope and grab it nicely so that the scope is not likely to slip in the ring. With the tollerances for the Picatinny system in use by manufacturers, a scope that is set-up on one "one piece rail" can be moved to another "one piece rail" of Picatinny standards. For this to happen, the rings and rails have to meet "Picatinny" standards. Glen Seekins Rails and rings do that. Others that might, (I do not have direct experience with them,) but I believe Near Manufacturing and Badger Ordinance do that too. But I can only speak for what I have seen with Seekins stuff and with the Leupold stuff.
Hope it helps.
Paul