Shoes

Shoes

Buying Dance Shoes for Both Lead and Follow: 

Dance shoes must have a solid “shank”, have a balanced centered heel, solid heel support (strap them down!!!) and soft supple coverings for flexibility of the toes.
Avoid “character shoes” which do not have the support you need. Also avoid too much braiding or other detailing over the toes - these shoes do not stretch well.
Avoid satin and other materials that cannot stretch. Get a flexible material or style; I recommend a soft leather, and make sure the shoe is a little tight.
Look for a smooth hard leather bottom or “chrome suede” bottoms.
Look for durability. Plan for stretching, ie. it's okay if they are a little tight. 

Followers:

Avoid open toed shoes for a minimum of your first year, but really would recommend open toes only after a few years of solid dancing. 
Stick with a 2” or lower heel for your first year. Also, feel free to avoid wearing heels - I prefer to support healthy feet so we can dance longer!
Buy a backup low or no heel flexible jazz or ballet flat for when your feet get sore. Worst case use socks.
Learn foot exercises to strengthen your toes, feet, and ankles; and to avoid severe injury to your feet.

Leaders:

Aside from ballroom shoes; often leaders can find sneakers or adapt their most comfortable shoe into a dance shoe. Find a good cobbler. Have your soles resurfaced with chrome suede, and voila! You’re good to go. Pumas, Adidas, and any other soft leather sneaker are ideal. Also don’t be afraid to check out jazz shoes.
Don’t fuss about “stylizing” your walk (that’s what show dancers do...) just walk normal heel-ball. 
Learn exercises to strengthen your feet and ankles, too - this gives you better control and connection with the floor.