Brakes "skip" as I press down. Whats goin on?

Have you checked the brake fluid level? Have you had any recent brake work? How's the brake pedal height?

I just bought the car last week so not sure.

That's exactly where I was headed. It sounds as though you might have a leak, it starts to stop on initial pressure then fluid escapes releasing pressure.

Check fluid level, and look for a potential leak.