Final Cut Pro has been the staple for nearly all editors in the industry for some years now but I hear many rumours running around that Premiere is about to take over so you're right to edge towards that one. Both programs will do everything you want, absolutely. If you get Premiere then there's a chance that you can get extra handy programs like Photoshop, a transcoding program a I think a colour grading program, but obviously you're shelling out a few more clams for a package. If you go for Final Cut, be wary, the latest one is universally hated by everyone (FCP X), FCP 7 tends to be the current favourite.
But yeah, you're definitely set to make any videos you want with premiere or FCP, don't worry. You just need to get to grips with them and learn all teir little tricks.