Newbie looking at FCPX

I currently use Camtasia for Mac for very basic video and also have a pro-sumer video camera all for creating web tutorials. I have an iMac with 2.66 GHz i5 processor and 8GB RAM. Do you think I could make use of Final Cut Pro on my machine for the basic video I described? I'd do some overlaying of both video and audio but (in my naive thinking) would be fairly simple.

It should work fine, but don't take my word for it. Download the 30 day free trial and see for yourself.
Also, I recommend that you take the time to learn it. There are great tutorials online, such as the free one at Izzy Video, that will help you get up to speed.

I'd also look at ScreenFlow over Camtasia for the Mac.

+1 to ScreenFlow.

Additionally, I'd stuff more RAM in your iMac. The 8 gig are a bit on the meager side.

Great information guys. Screenflow looks like a good option to check out and Final Cut Pro as well. I appreciate your input and know about the free trial option which I'll venture out and do.

Much obliged for your help.

+1 for adding more RAM to your iMac. That will make your FCPX experience much better.
I don't know what GPU capacity you have but probably that is a weak point. Since it's an iMac there isn't anything you can do about that, however, since it sounds like you're doing short form projects transcoding time shouldn't be a problem.

I have an old MBP with much weaker specs and it works fine for basic stuff. I mainly use it for organizing footage. For what you want to do, your machine should be fine. More RAM always helps, but will probably not make a critical difference. The easiest thing to do is download the free trial and see how it performs. FCPX works amazingly well on older machines.