Both iMovie and Garageband are extremely capable software so don't cut them short. If you are running Snow Leopard 10.6.8 you can upgrade to Mavericks however Mavericks uses more system resources. If your machine has 4GB or more of RAM installed it should run Mavericks just fine. It won't be as quick as a new iMac but it should be OK. If your iMac has less than 4GB then I would STRONGLY recommend upgrading the RAM to 6GB which is the max your machine can accommodate. Newer iMacs can handle up to 32GB. If you do not know how much RAM is installed then click the Apple Symbol in the upper left of the display and click About this Mac.
Since it is an older machine with a (comparatively) slower processor, any video work will be slower and that has nothing to do with Snow Leopard vs. Mavericks. For video editing/rendering/burning, the fastest, bestest processor as well as lots of RAM will speed things up. I had a 2006 iMac and it did my video work ok - I just got used to walking away and not using it while it was rendering or processing. I now have a top of the line 2010 and lots more RAM - video work is much faster, but it still takes time - that is the nature of the beast so to speak.
As for SL vs. Mavericks: if you don't need the bells and whistles of the latest OS including iCloud integration, etc., Snow Leopard will be fine. 4 GB RAM are great for SL; for Mavericks, it is considered the minimum (8 - 12 or more would be better for video work). The latest iMovie version 10 appears to be less user editable and more for fast processing and cloud integration - lots of choices to send to Youtube, Facebook, etc, etc, but not enough options to export so the movie can be burned to a DVD or imported into Final Cut or iDVD. I've tried it twice and will do so again, but will stick with the older version for now.