If you just get a triple, even the very common 52/42/30, you'll have a much lower gear than you do now, 34 inches versus 47 inches. If you just get a compact 50/34, it won't be so low; you'll get 38 inches. With either one you can go a lot lower by going to a rear cassette or freewheel (forgot which one your bike uses) with a big cog in the 30 or 32 tooth range. That will get you (for the triple and compact respectively and the 32) 25 inches or 27 inches (not very different!). Depending on how hard your hills are, you might want to go even lower as you return to riding - 19 inches is a practical "lowest possible gear," needing you to come up with a 24 front and 34 rear. This is possible with some triples, but impossible with any normal compact double.

I'd suggest getting a triple that can take a granny ring as small as 26 teeth. It will give you the most flexibility. My brief recollection of Austin is that the hills are steep. You might need all that extra depth, but only you can say.