I went ahead and dumped the private key. It starts with a capital L. I thought it was supposed to start with a 5. What does that mean?
This is okay, as there's actually two types of private keys, uncompressed (WIF starts with a 5) and compressed (WIF starts with a K/L).
The only difference is that the compressed keys are suggesting to generate the address from a compressed public key, while the addresses generated with the ordinary keys are generated from an uncompressed public key.
If you have the private key of any format, both the compressed and the uncompressed address are yours.
By the way, if you use bitaddress.org (I don't recommend it though, if you ever use it, DOWNLOAD RUN ON AN OFFLINE MACHINE), keep in mind that you have to use the compressed address in the Wallet Details section.
Ok, so now that I have the private key, what specifically(in the most layman terms possible) should I do with it to safely get my coins into a new wallet? My knowledge is clearly lacking and I don't want to screw this up obviously. I have a breadwallet and just started a blockchain wallet. Can it(or should it?) be done with either of these? I don't intend to ever use my old desktop again(aside from photo storage etc), I just want to safely get my coins out ASAP.