I'm not sure what ASIO is but MIDI is, in general, a system used to communicate between computers and electrical sound instruments(electrical piano keyboard for example)... it gets more complicated than this i assume.
Unless you need a good sound card for professional purposes, i would only really look at the amount of audio ports it has and the brand (Creative are pretty good). Things you may want to look at:
SPDIF: used to connect stereo systems, dvd players and such accessories...
Sample Rate: A lot of audio cards come with 48khz and 96khz, but again if you need to output audio or media at a higher rate for better quality go for the more expensive 192khz.
O/S: If your using a 64-bit system i'd check to see if that audio card has 64-bit support
Interface: Its up to you whether you'd like a PCI interface or a PCI-E. PCI-E's are a bit faster but PCI's are fine as well.
In general, if your going to use a card for surround and gaming... don't bother with SOME of the specs besides the ones i recommended you look at and get a cheap Creative card.
Hope i helped ;)