Near rings and bases are about the best in terms of quality. More money then others, but are well worth it.
Another good choice would be Seekins Percision rings. They are aluminum rings, so light weight if weight is a concern. I have heard good things about these. Never tried em myself, so can't say one way or another. Not sure if he makes bases or not.
I have used many different Ken Farrel 1 piece bases and like them. Not true Mil spec, but work well enough for me. They are a weaver style base so you will need weaver rings.
Cheaper but great rings are the Burris Signature rings - the ones with the plastic inserts. The inserts allow for additional MOA to be added without changing the base. I have used these on a 300 RUM and they held very well.
I have recently purchased a set of TPS rings. (Tactical Percision Shooting) They are the tactical version. I think they have a hunting version, but not sure. These things are SOLID and HEAVY! They are supposed to eliminate scope cant when tightening the rings up. They are also supposed to hold well due to about a 98% scopr/ring contact surface. Is this true or not, I do not know. I look forward to trying them out. I just have them mounted so far, so no comment on performace as of yet. TPS also makes tactical style bases as well.
Warne rings and bases are good as well. Only used a couple sets of 2 peice rings, I liked them from the little bit I used them.
Nightforce also makes rings and bases. There is also the Badger Ordinance option, but to much money for me.
I would heavily recommend Weaver style rings instead of the double dove tail ones.
Personally I would go with the TPS rings ( I like the look of the tactical ring they make ). The Burris Signature are another great choice if you are on a tighter buget - about half the cost. The TPS website is http://www.tacticalprecision.com/
I like the look of one piece tactical style bases, so I would recommend those. I would say either the Ken Farrel or the TPS base. I was thinking about trying one of the TPS bases for my remingtons, but they all have Ken farrel bases currently.
These are just my opinions of course.
Ultimately it will depend on your budget.