This is just simple quick and dirty, but you'll get the point

I'm not going to go in to very much depth on using the pen tool, for more on that, see here-
Vector Tutorial
Vector Tutorial
Why would you want to make vectored paths for your insignia? Several reasons; you can reuse the paths, copy and paste them between files, enlarge them or reduce them without loss or sharpness (more on that), fill them with any color and refill them at any time, modify them to suite distortions on a skin and best of all, you can spend a lot of time to make them perfect and then never need to redo them again.
Sounds good huh?
*You could do these in Illustrator or Freehand, but you'd still need to bring them into Photoshop in the end.
About the sharpness, this will, like everything else, depend on the resolution of your file you're working on and the end size of your skin. If you want then SHARP down to the pixel at a specific size you'll need to make or modify the paths to that specific size of course.
*If you've got a font making application you should be able to use these vectors you've made in Photoshop and make a font from them...but, if you have this capability, you probably already know how to do it :P
Here is a quick lowdown how-too:
It's easiest to just find some art to copy for starters. If you want to get really specific you should be able to find exact measured drawings of the insignia you want to do. In this case I just started out with a simple (and not too completely symmetrical it turns out) image from the internet.

The best starting point is to use guides and find your center and all other measurements, outside width, etc.
Once you've established your center, you can use the ruler or my favorite, the marquee tool to make sure all your measurements are equal left/right/top/bottom. These, combined with "snap to guides" (view > snap to > snap to guides) makes easy work for later.

I usually measure out guides for any straight edges and any shape boundaries.
Once you've got all the guides you need you can start drawing your paths.

I started out using the circle/oval shape. Make sure it's set to make a path, not a fill. To make a perfect circle, hold the shift key down while dragging the corner of the circle. Of course, if you've arranged your paths correctly and have "snap to guides" selected, it should come out perfectly round.

In this case I want concentric circles because my paths will allow me to make any combination I might want. The quick way to do this is to copy, past, and select edit > transform paths > scale. Once that's selected hold down (for Mac OS) command-option-shift and drag any corner box until it's the size you want. The circle will be absolutely concentric if you've done it right.