For weightlifting, you generally want to have shoes with a flat sole. This is useful for deadlifts, squats, and olympic lifts. People often lift in Chuck Taylors or Nike Frees.

If you're serious about lifting you should look into getting real squat shoes.

http://www.exrx.net/WeightTraining/Weightlifting/WeightliftingShoes.html Helpful article by Rippetoe and Kilgore. When you're doing a heavy squat, you don't want a shoe that will compress under load and prevent you from driving through the heels.

My shoes: an older version of http://www.dynamic-eleiko.com/products/adiStarFRS.html. Love them. You can often find them on sale. Adidas shoes work great for a lot of women because they're relatively narrow.

Other brands: http://www.vsathletics.com/product.php?xProd=1301.

Starter shoe, relatively inexpensive. http://www.roguefitness.com/store/rogue_dowins.php Good fit for wide feet. Have heard complaints about quality. Over at http://www.werksanusa.com/products-shoe-shirts.asp:

Wan - new player on the scene, Chinese made.
Risto - Russian made. Comes in pink! You can alos order custom colors over at http://gwenweightlifting.blogspot.com/
Weksan's own brand - haven't heard much about these
Werksan Do-Wins
http://weightliftingshoes.ca/index.html - Canadian business, will custom make shoes from tracings of your feet if you're a hard to
fit size

http://store.nike.com/index.jsp?country=US&lang_locale=en_US&cp=usns_KW_071608_FroogleCSE&l=shop,pdp,ctr-inline/cid-100701/pid-186718/pgid-262321#l=shop,pdp,ctr-inline/cid-100701/pid-186718/pgid-262321 - produced for the last Olympics and have a plastic, rather than a wood heel. Some people love them, some people hate them. Difficult to find, only available in teeny sizes at Nike or on ebay.

Anyway, there it is. If you don't want to invest yet (but you should really start thinking about it :) ), go for the Converse All-Stars because they're a lot less compressible than typical running shoes. You don't need the hightops, in fact, a lot of ankle support will interfere with your depth on your squats.