Clarifying Attack Type for PW Type

[Xanadrel]

My main question is, since my password is a bunch of random characters (for example: 8Gy69BZs), would I want to try to use a Brute-Force style attack for that?

Yes and no, for completely random passwords there is not really other options, but for wpa (which is slow) bruteforce can take between long and too late you died.

oclHashcat64.exe -m 2500 -a3 capture.hccap ?d?d?d?d?d?d?d?d

Am I correct in understanding this will run through every potential character and eventually should find my example password above?

No, read more about mask attack/charsets.