shoes
Having reasonable footwear for tango can make all
the difference.
Your shoes should be comfortable and allow you to pivot easily
on the ball of your foot. Usually this means something with
a smooth sole, like a dress shoe.
Sneakers, hiking boots, and bare feet typically stick
to the floor and make it difficult to pivot in place
on the ball of your foot - besides making tango
moves difficult, this can hurt your knees.
Thick socks may work, though they can be too slippery.
Although it's common for followers in tango to wear
heels, and you certainly may, they are not necessary
for our class. Moreover, since we encourage all
students to lead and follow, heels can be problematic
since they make it difficult to lead.
We recommend dance sneakers or other smooth soled shoes.
If you want heels, character shoes are a reasonable
choice (see below for an example).
online

The Sansha Salsette is a nice dance sneaker for tango,
with suede under the ball of your foot for a good pivot and a rubber heel for traction.
$33 from Amazon. (The sizing is off though - order about 3 sizes larger than your regular shoe size.)
Other styles of Sansha dance sneakers are also popular for tango.
If instead you'd like something with a heel,

this
New York T-Strap
2" heel character shoe for under $40 has worked for some past students.