Someone correct me if I am wrong, but aircrack-ng is going to be used to capture the packets over a wireless network to capture packets to break the WEP, WPA/WPA2 key, so yes you will need a wireless adapter if you don't have one built onto the motherboard. But the adapter needs to have packet injection capabilities. This link can help you determine if one you do have is compatible with aircrack-ng. Your best bet is to get one of these from Hak 5 to help with your endeavors.
Look into this program. Works great when you have captured the handshake. http://hashcat.net/oclhashcat-plus/
https://hashcat.net/wiki/doku.php?id=cracking_wpawpa2
That page explains how to get the handshake into ocl
kaspersky has a free to download live linux cd that is meant for this purpose and has easy to use preloaded tools for removing viruses outside of windows. I personally use Puppy with some preloaded tools that was made for me by a coleague for this, that I use in my shop
EDIT: sorry forgot to post a link https://support.kaspersky.com/viruses/rescuedisk
Haven't tested with injection. ~~I'll give that a try sometime this weekend.~~
edit:
I followed the instructions on this page to do an injection test and found that it does work. http://www.aircrack-ng.org/doku.php?id=injection_test
Under the Basic Test area of the site I ran the aireplay command and pretty much got the same results saying "Injection is working!". Make sure to put the card in monitor mode before running the test.