I'm my opinion you should get both, but start with the CompTIA ones first! Aside from being cheaper and easier to obtain they will prepare you for future certifications. Most reputable computer companies won't even look at you unless you atleast have your A+, so I'd personally start out with A+ then perhaps Network+ and Linux+, for example. Once you have a few of the more basic certifications under your belt then you can aim your sights higher.
ArchAngel is right, you need to start yourself on the bottom of the hill and then work up. And number of people that have a advanced cert from Microsoft and others really have no idea how to do anything else than what is inside their narrow field. if you start with the basics first you will find a lot less surprises when you get your first job. And it will be easier for you to get a job, remember its easier to get your foot in the door at ground level than for jobs in the admin level.