I think the advice you've already gotten is sound -- I don't think I'd want to learn fixed and clipless at the same time. My first (and only) fixed gear has TIME ATAC clipless pedals, and I started riding it with them, but I was quite thoroughly used to the clipless by then.

I actuallly tried fixed with platform pedals and toeclips once, and I found it a lot harder than clipless -- the ATAC pedals can be clipped into on either side, so you don't have to flip the pedal over. I found it really difficult to flip the pedal to get my feet into the straps on a fixed.

But of course, like anything, practice makes perfect.