There are a lot of really high quality products out there...certainly ones with big price tags as well. Having been in your position recently...I purchased a Ferrell 20 m.o.a one piece base from SSS..about $70-$80 with shipping...They are a sponsor of this board. It might simply be a myth...but supposedly a one piece might add structural rigidity to the action.
As far as rings...stay with bigger names...try not to skimp too much...you don't want to mess up your tube with ill fitting rings. I've got LEupold QRW's on one...NightForce Aluminum on another....and some higher end Burris on a couple.