I think I should use a different circuit for the light and the outlet so I don't loose the light if my outlet gets shorted.
This is always a good Idea. As far as the lighting on the GFCI, That's got to be your call. As Dspark says it will give you more personal protection fron shock, but if the lights go out on you (nuisance tripping) will that pose another type of hazard? Only you know the circumstances of your room layout and it's probable usage.
And, yes, new circuits would be called for. An inspection (by Electrical Inspector or consultation with a Licensed Electrician) is always recommended for your personal safety and it could save you money. If you do not do things according to code rules you may end up having to tear things apart later on.
I see it happen all the time!