Proper shoes are a must for dancing. Proper shoes allow you to pivot on the ball of your foot, glide across the floor, and support the foot correctly for dancing.
Proper shoes are an important investment to avoid injured joints.
Above all, avoid running shoes or any shoes with a gum rubber bottom!
Ballroom and Latin Shoes
Most leather or suede bottom shoes should be adequate.
Shoes specifically for ballroom dance, however, are best.
Until you've obtained proper shoes, you can dance in your socks.
So called ballroom practice shoes are best for class. No need to spend a lot on glitz.
Dance shoes should not fit loosely, but more like a comfortable glove. You're dance shoe size might be ½ size lower than your normal shoe size. But note that manufacturer sizes can vary so it's best to try them on in person before buying.
Local
Ballroom Connection (Sunnyvale) has a huge variety ($75 and up). RECOMMENDED
TOMS shoes have sufficiently slippery rubber soles.
Ballroom Connection (Sunnyvale) carries swing shoes and jazz sneakers. (Beware: the Ballroom Connection staff have been known to miss-direct our students to Ballroom practice shoes for swing. Ballroom practice shoes are not recommended for swing dancing!)
An old pair of sneakers with worn slippery soles from your closet or a thrift shop.