a primer generally enhances and prolongs the time makeup stays, makes application smoother and easier, and fills in slight dips or wrinkles in the skin. a base is generally the same thing, although, as mentioned above, sometimes bases work mostly towards color enhancement or to change the color slightly, rather than prolonging the wear time, if that makes sense.
eyes: urban decay primer potion is by far the best eye base i've tried, and i've used several. apply a thin film to the lid, blend with finger til invisible, wait about a minute to dry, then either apply a color base (shadestick, paint) or just apply your eyeshadow/pigment as normal. i have never had a problem with ANYTHING creasing with UDPP, even pigments. i usually use shadesticks on top of the UDPP, just to make color a little brighter, then apply the eyeshadow or pigment. paints work too, i guess, i just have never had as much luck with them. mac prep and prime eye is nowhere near as good as urban decay primer potion (UDPP), nor is l'oreal de-crease, or the too faced primer (first and second base, i think).
face: i personally like smashbox photo finish primer better than mac prep and prime skin, but make sure you use it sparingly because a little goes a LONG way. also, it works so much better if applied with fingers, versus a brush, i've found. primers really do help foundation look better and stay longer, with the one exception of studio fix fluid. i can't get it to work with a primer, and i don't know wjy. so far, i just use it with moisturizer underneath.