I wish to store UUIDs created using java.util.UUID in a HSQLDB database.
The obvious option is to simply store them as strings (in the code they will probably just be treated as such), i.e. varchar(36).
What other options should I consider for this, considering issues such as database size and query speed (neither of which are a huge concern due to the volume of data involved, but I would like to consider them at least)
You have a few options:
The upsides and downsides of each approach is based on how you're passing the UUIDs around your app -- if you're passing them around as their string-equivalents, then the downside of requiring double the storage capacity for the VARCHAR(36) approach is probably outweighed by not having to convert them each time you do a DB query or update. If you're passing them around as native UUIDs, then the BIGINT method probably is pretty low-overhead.
Oh, and it's nice that you're looking to consider speed and storage space issues, but as many better than me have said, it's also good that you recognize that these might not be critically important given the amount of data your app will be storing and maintaining. As always, micro-optimization for the sake of performance is only important if not doing so leads to unacceptable cost or performance. Otherwise, these two issues -- the storage space of the UUIDs, and the time it takes to maintain and query them in the DB -- are reasonably low-importance given the cheap cost of storage and the ability of DB indices to make your life much easier. :)