Hi Ron,,
Welcome to the forum, nice to have you with us. I have that same scope, actually I have a couple of em, they're pretty good. As for the rings that they come with,,,, they won't hold on the Shadow 1000.
The advice you received from GAMO about cleaning everything, and I mean everything, really well with denatured alcohol and also using blue loc-tite is sound advice. I do that on every scope I mount.
There are a number of good mounts out there to choose from, some expensive and some not. I like Accushot 1 piece mounts, available from Pyramydair.com for around $20 bucks, and they have held well on every rifle I installed them on, including my Shadow 1000's.
BKL also makes an excellent line of scope mounts, although they are a bit pricey (but well worth the money). Do a search on GTA and you'll come up with a ton of info on scopes, mounts, advice, etc. I'm sure the other guys will chime in also here and give you their advice as well.
Again, welcome to the forum,,, and if you hunt with that shooter of your be sure to post your hunting stories and pics in the "Hunting Gate". We just love hunting stories and pics.

Jeff