I've just purchased a Washburn Travel Guitar. I know I'll never get full guitar sound out of it, but I was wondering what strings I could / should get to (perhaps) maximise this little guy.
The same string choice compromises apply with a travel guitar as with any other guitar.
So you need to choose.
If the purpose of this travel guitar is to practice when you're away from your full size guitar, then I would recommend having the same gauge strings on both. You want to replicate the feel of playing, even if the sound is less full and loud.
If the travel guitar has a shorter scale, then it may be worth using slightly heavier gauge strings, to replicate the tension on your main guitar. Use the D'Addario String Tension Guide to look up the tension of your existing strings, and what gauge would approximate the same tension on your travel guitar.
As for factors other than gauge -- the precise alloy used, and so on -- I'm going to lay my cards on the table and say that the differences are too subtle to worry about.