I cannot be sure about checking the ASIO support but look at:
On your Device toolbar (if it is not on you may turn it on with menu View > Toolbars) try all the options–something may refer to ASIO. Next, from the menu pick Help > Audio Device Info… something there may refer to ASIO. Penultimately, just before you quit, from the menu pick Help > Show Log… something there may refer to ASIO. Finally, you could try installing ASIO4All–it might show up as an ASIO device (it does on my system).
I have no recommendations on sound cards, try Sound Card Reviews and Multi-channel Recording in Audacity but take all there with a grain of salt! What do you wish to accomplish with Audacity, ASIO and a sound card? What is your experience level as a sound tech/engineer? Do you already have audio gear like mixers, compressor/expander/limiters etc. which you might want to integrate into the solution?