I get asked about shoes a lot. So here is a loose guide.
Most basically, if you are beginning and don't have any shoes that fit the below criteria, you can dance in socks! :)
• The most important thing about tango shoes is that they allow you to pivot, and have a good connection with the floor. So thin, soft leather or suede soles are best; the sticky rubber soles on most athletic shoes are worst. Avoid rigid platform heels; they raise your center of gravity and make it harder to balance in pivots, also will prevent you from articulating your feet when you walk. Avoid also slip-ons; they should have a strap or tie so you don't lose a shoe mid-dance!
• If you're looking to buy a new pair, beware: tango shoes are EXPENSIVE, especially on a student budget.
Leaders: I know less about your shoe needs - sorry! BUT I do know that you can wear either traditional tango shoes, which have a bit of heel - or dance sneakers (see below). Or, for more options, can glue suede onto the bottom of thin-soled sneakers (e.g. Puma) or flat-bottomed skate shoes.
Followers: If you have been dancing for a while, and you want some dedicated dance shoes, but aren't ready to shell out $110+ then you can start by getting a pair of generic ballroom shoes. For example, I danced in these Very Fine heels for the first year: https://www.discountdance.com/dancewear/style_9691.html?&pid=7972&Shop=B...
For Formal Dance Shoes: If you're ready to invest in a pair of real tango shoes, the best place to try them on is at a festival. (List of regional festivals to come...)
If you're willing to buy online, there are myriad options. I would *always* contact the seller to make sure that you're asking for the right size.
The most popular brand of tango heels is probably Comme il Faut, which retail for around $2-300. Julia Bella http://www.julia-bella.com/ has quite an extensive collection online, and ships from MD, so incidental costs aren't as high as companies located abroad. (Anywhere in S. or Central America charges around $35 for shipping.) Felina Shoes has a slightly smaller selection, and slightly better sales, $15 for shipping... http://www.felinashoes.com/
If you are looking for something lower budget, Very Tango recently showed up on my radar; it is based in Turkey (which, surprisingly, has an incredibly robust tango scene) and charges $35 for shipping. I've never bought from them, but they seem to have cute shoes for the $120 range. http://www.verytangostore.com/all-women-tango-shoes.html?sort=priceasc
My FINAL advice is that you might look to Ebay for high-end lightly or never worn resale shoes. Lots of dancers buy shoes from Argentina or elsewhere and would rather resell them than send them back - so you can find good deals that way - sometimes even under $100!
That said - if you have unusually shaped feet (like me!) and can't 'buy off the rack,' Jorge Nel at Mr. Tango Shoes will do custom orders: http://www.mrtangoshoes.com/ It will also cost around $200. I am only sort-of satisfied with the shoes from them, and am a bit interested in trying this newish Mexican Company, Blüen, which seems to do custom for about the same price and has super cute designs: http://www.blueinshoes.com/
For long practice sessions (festivals, workshops, etc) I wear dance sneakers; they are a little clunky for formal situations, but very supportive and comfortable for long periods on your feet. They also have a smooth, plastic sole and pivot very well: http://www.discountdance.com/dancewear/style_P22M.html?&pid=4348&Shop=St...
Am just trying out something lower-profile (more nimble, less chunky) for late-night milongas when my feet are too tired for heels. Will let you know how that turns out :) http://www.amazon.com/gp/product/B017JMFU1A/ref=s9_simh_gw_g309_i1_r?pf_...
Although I've never used them, lace up practice shoes with heels are popular with a lot of followers: http://www.discountdance.com/dancewear/style_GO405.html?&pid=20063&Shop=...
Let me know if you have any further questions! Happy dancing... :)