If using a handheld system, you definitely want a few dives in before you start adding tasks. How many dives is up to each person. Once you are comfortable with your buoyancy, and have a regular process for checking air, etc. then you can start to add some tasks.
If using a mask mount, you can pretty much start right away as the camera isn't requiring any operator intervention aside from starting it at the beginning of the dive and stopping at the end.
I spearfish on a lot of dives. Profile pic was actually taken from a GoPro mounted on my head. I have it set to snap a still pic every 10 seconds or so while it is recording video. Most of those pics are crap, but I usually get a few decent ones every dive. Since I spearfish, my hands were already full, and I didn't care for the gun mounted setups as they shake pretty bad when the shot is fired.
I agree with what others have said. You will find that a lot of the video is shaky. As you get more experienced, you'll be able to correct for that somewhat.
Keep one thing in mind. Most of your video footage should end up on the "cutting room floor." Nobody wants to watch a 30 - 50 minute dive. Even if it's an awesome dive. 3-5 minutes should be plenty for most dives. Get rid of all the shaky shots and really just include the most interesting parts as well as a bit of lead up. I usually start a bit with descent, and include a bit on ascent at the end.