I use the Luepold Rifleman, weaver style mounts on my Handis
I have one other gun with weaver style scope rail, I use Weaver 4x4 rings - I like these rings for a weaver style attachment.
Without a doubt, avoid the ring style that is essentialy a band, that is tightened on one side only. As you tighten it, it tends to roll the scope, and getting the reticles level is a major PITA.
Also, all of my mounts are lapped first. I dont know how much it helps, but never have I noticed the both bottom surfaces were true without the lapping.