I always make a pale ale to start out, taking a guess as to the alpha acid that is typical or average of the hop variety. Then if it turns out too bitter, call it an IPA. If not bitter enough, call it a blonde ale. From there, when you make the second and third batch, you will be able to come amazingly close to figuring out the true alpha acid based on taste alone.
I also sometimes like to mix my homegrown hops (at least the bittering addition) 50/50 with a known similar alpha acid variety. Then I don't need to "waste" as much of my homegrown hops figuring out the alpha acid.
Homebrewing software such as ProMash, StrangeBrew, BeerSmith, etc. is key to figuring out your alpha acid based on taste. First assume something, then iteratively adjust it based on taste for successive batches. You'll come really really close on the third or fourth batch, and very reasonably close even on the second batch.