Should I beta test before a launch or post launch?

That totally depends on the product and the receptivity of your early adopters. I've done both and in some cases, even have no beta, but have beta [test] clients, with a view to building the technology as a co-production with their help. This means extensive, micro-Lean Startup activity which continually creates features and enhancements. A beta can be useful for a pipeline here. So your beta clients are early adopters and this stuff then goes into mainstream use after a while. Facebook does this and so do Hootsuite.

Beta launch is still a launch, and then relaunch and relaunch as many time as you need. But yes, calling a launch "beta launch" means you will get away with some bugs and issues :)

If you're launching a SaaS and assuming it'll be a paid service, you can do a beta launch, being explicit that you'll either give free service or a reduced price in exchange for feedback. When you've collected enough feedback and ensured your product works perfectly, then you can do a general launch with normal pricing.

We experienced that it really helps! Thee are more errors and improvements as you think.