So I've tried FRAPS, Jing, Snagit and Camtasia
Fraps is easily the best performing one, especially seeing your framerate, and it's lack of CPU Usage while playing. The filesize while large shouldn't be a problem at all, if it is due to space on your computer you need to clear some stuff out

If your computer is too small you can easily buy a cheap external harddrive. There is a FB page called '10 ways to save money as a student without having a job' and I regularly see 2TB harddrives for like 25 pounds on there. Most laptops these days come with plenty of storage to use FRAPS though, and a rendered video takes like 95% of the filesize out. Even if that is worrying you there's all sort of software - eg Handbrake - that will reduce filesize with no discrepency to the video file itself.
Jing - Poor framerate while using, I liked that you could pick the section of screen meaning you can record just browser footage but I wouldn't pick this up.
Snagit - when it records video it only takes the first frame and records the audio after that, it could just have been my experience but don't pick this up.
Camtasia - I like using Camtasia and being able to choose the recorder size and able to record browser usage is useful, and it comes with it's own editor but thats a massive hindrance to me because I use a third party editor to edit my YouTube videos which means I have to render out of Camtasia Studios 8 into an mp4 as it saves the auto as a .trec and .camproj and rendering times can be absurd. Also I notice it uses more CPU than FRAPS meaning lower framerates in open games. I only have a laptop however, this should be a void point to anyone with a dedicated gaming system.
I'd say go with FRAPS but if you're absolutely against it pick up Camtasia because it does the job you ask.