welcome aboard!
Technically you can run up to a 265 on the stock rims. Some guys have run 285's even though they are technically too wide with no noted wear issues.
I have a rough country 2inch lift(got a deal used) with Z71 springs that I love. Most of my offroading is beach driving as well. Before I got the lift I could feel myself bottoming out going over ruts but I rarely have that problem now.
If I were in the market for a new lift now I would get one from MarkMC(board member/vendor). It is about 3 inches front and I think 2 in the rear. You can also get the wheel spacers from him as well. That would let you run a 265/75/16 with little to no trimming or a 285/75/16 with a good amount of trimming. From the sound of it that would likely be all you would need.
here is a link to a chart that gives you a good idea of lift etc needed for the appropriate tire size.
viewtopic.php?f=15&t=2290&p=38841#p38841Right now I'm running the 2 inch lift with 255/70/16. I ran those tires with no lift but it would bottom out. I plan to get spacers and 265/75/16 the next time I need tires.
If you aren't in a rush you can many times find what you need cheap/used in the classifieds here or on trailvoy.
Also if you get spacers/adapters that convert to the 6X5.5 standard chevy bolt pattern, keep your eye on craigslist. Since I have no extra money I seem to find deals on there for silverado, tahoe and toyota rims with used 265/75/16 reasonable all the time.