I have an older Marlin 444 and found I have the Weaver 64B bases and I am wondering if only the Weaver rings will fit this base?

If this is a poor choice what base/rings should I order?

I can't help you on your current rings/base question but I just put Warne rings and 2 piece bases on my Marlin 45-70. They are rock solid and I really like them.

I use the Talley Lightweight two piece on my Marlin levers that I scope.

Burris Signature dovetail rings........

Leo or Weaver turn in style base

I use the Weaver base which I then cut the back end off of and make a three screw base. I install a Williams Fool Proof receiver sight for a backup. I never have had to use the backup because of a scope problem but it lets me borrow the scope when needed and still have a useable rifle. Weaver rings are great rings, but I like the rings with two screws on each side of the rings. The rings with only two screws on one side are hard for me to align the scope vertical. I've never had a scope move in either of these rings. They are not very sleek looking but they do work.