Great questions!
First, I would suggest beige for sure—least likely to show under any color/fabric. That being said, the idea behind any shaper is not to squeeze you into thinness, but to pull in and smooth out lumps/bumps for a more aesthetically pleasing look under clingy fabrics. Even if your thighs, etc. are technically smooth, under a clingy or body skimming fabric the most minor lumps/bumps can be magnified, so that’s the general idea—to mimimize that effect.
So, like anything else, it’s about getting the right size. Try it on if you can, or be sure to use size charts and measure your body to get the best fit—it should fit comfortably (well, reasonably comfortably) without squeezing (which will cause rolls at the top and bottom, which kind of defeats the purpose. Remember, it’s about smoothing for a more flattering fit - not making us two sizes smaller.
Next, figure out how extensive you want the shaping to be—meaning, depending on your tummy, will you need a shaper that extends up to the bustline (which, if you’re short waisted, might not work) or something less drastic (the only shapers I’ve used extended from mid-thigh to just under the belly button, and were perfectly sufficient to smooth out the tummy and hips).
Finally, a good shaper will be well constructed—I would look for double stitched seams and the fabric should have some stretch obviously (lyra/spandex—up to 20% I would say) but not too much—you don’t want it to stretch out of shape and be useless. Also, make sure the seams are nice and flat, or look for a seamless version.
On a budget, I would check out the ASSETS line at Target (it’s a budget line by the same folks that make Spanx, which, of course, the celebs swear by). http://www.target.com/ASSETS-Sara-Blakely-Unbelievable-Underwear/dp/B000F8EC8I/qid=1214308726/ref=br_1_10/601-2658249-0418506?ie=UTF8&node=110197011&frombrowse=1&rh;=&page=1. Hanes also makes a reasonably priced line (http://www.target.com/Hanes-Thigh-Slimmers-Black/dp/B0012ZZYBC/sr=1-7/qid=1214309431/ref=sr_1_7/601-2658249-0418506?ie=UTF8&index=target&rh=k:body shaper&page=1) that might be worth looking at.
Also, never underestimate asking your friends/family for brands, styles they like.
Hope that helps! If anyone else has suggestions . . .