Recording set-ups in a nutshell.
Left we have the regular way non-CFW option and right we have the pirate way.
Note. images are randomly taken from google and setups don't need to look exactly like this.

Left should be self-explanitory
PSP> Video cable> Video Card> PC> Video capture software
Right
PSP with CFW, remotejoy(lite) plug-in> USB cable> PC>
Lineout > soundcard> Remotejoy interface> Screencapture software
Pros and cons
OEM
+Doesn't require an exceptionally strong computer
+Easy to set-up
-More expensive
-Video quality is quite bad unless you capture with a component set-up
CFW
+Cheap
+Video looks better than component
-More taxating for your computer than the 1st option, this point is moot if you don't have a dinosaur computer
-If you're new to CFW's and plug-ins you'll need to do quite a bit. Also plug-in compatibility with the pc software is a pain.