(more info coming soon)
U Michigan's Ballroom Dance Club has put together a great set of pages with descriptions of the dances and info and videos of the steps: click here for them.
Disclaimer: This is in no way an advertisement for any particular company. This is meant to give an idea of what features to look for when shopping for dance shoes. There are many variations in fit and taste, so keep in mind the shoes should fit snuggly and comfortably and you should like them too. :)
Thanks to Aurora for putting this section together!
Above is a typical ladies' Latin dance shoe (for Rumba, Cha Cha, Samba, Jive, and Paso Doble). The one shown is Dance Naturals brand* with either a 2.5 or 3 inch heel. (I'm not sure which, but those are the usual heel heights for Latin shoes.)
Above is a typical ladies' Ballroom shoe, sometimes called a court shoe (for Waltz, Tango, Foxtrot, Quickstep, and Viennese Waltz). The one shown is Dance Naturals brand*, in either a 1.5 or 2 inch heel. (Those are the typical heights for Ballroom shoe heels.) I highly recommend versions with a somewhat rounded toe, since they squeeze the toes less and still look nice.
Above are practice shoes from Stephanie Dance Shoes*. These can be used for both Latin and Standard dances (although they feel less like the Latin shoe). These are a great option for when you are first learning and want to get one shoe. Also, these are great for whenever you may dance for more than 1.5-2 hours at a time, since they are usually quite a bit more comfortable. People don't typically use these types of shoes for competitions or exhibitions, so that is a limitation.
Heel height: If you're not used to high heels, don't be too apprehensive about dance shoes with heels. The heels on dance shoes are placed better than those on fashion sandles, etc., so they are actually much easier to balance in. Plus, the heels complement the movements and steps for the follower very well and you get used to them very quickly. If you feel uncomfortable though, consider starting with a good practice shoe, or perhaps choosing the lower ends of the spectra, i.e. a 2.5 inch Latin or 1.5 inch Standard shoe. Shoes with heels much lower than that are sometimes not as well constructed, since it is not as common for female dancers to use those shoes.
Above is a typical men's Latin dance shoe (for Rumba, Cha Cha, Samba, Jive, and Paso Doble). The one shown is Dance Naturals brand* with either a 1.5 or 2 inch heel. (I'm not sure which, but those are the usual heel heights for Latin shoes.)
Above is a typical men's Ballroom shoe (for Waltz, Tango, Foxtrot, Quickstep, and Viennese Waltz). The one shown is Dance Naturals brand*, in a 1 inch heel. (That is the typical height for Ballroom shoe heels.) You can buy Ballroom shoes which are shiny or matte black; I recommend matte for your first pair. I also recommend buying all-black shoes rather than white ones.
Buying your first pair: If you only want to buy one pair of shoes, I recommend buying a pair of Standard shoes rather than Latin shoes since Standard shoes are more stable (having lower heels). But it's nice to have both.
Get advice: Ask for advice from experienced dancers, club officers, or instructors. Be careful about relying on dance store staff; if the store sells mostly items for ballet or other types of dance, it's likely that the staff won't know much about ballroom shoes.
Choose a good fit: Ballroom shoes should fit more tightly than street shoes. Your toes should really come to the front of the shoe (for closed-toe shoes), and your feet should not slip around at all inside the shoe. Also, the leather will stretch some over time. It's common to buy shoes 1/2 or 1 size smaller than your normal shoes.
Find a bargain: A lot of cities don't have good (or any) ballroom shoe stores. If you visit a bigger city (especially one with an outlet store), take advantage of it. If you go to a competition, check to see if there will be vendors there. At shoe stores and competition vendors, you may not find great bargains, but you can at least try on shoes and get an idea of what you need. Search for outlet stores and online discount retailers, and ask other dancers for recommendations. Many online retailers will let you return shoes for no charge if they don't fit, so ask an instructor or experienced dancer about the shoes before you wear them if you're not sure about the fit.
* Dance Naturals shoe images are from Dance America's website. Stephanie Dance Shoes images are from Feather Dance Shoes' website. The images are copyrighted by the respective companies and are copied here with the companies' explicit permissions.