There is a very small risk that a betta will get sick after eating freeze-dried bloodworms. Especially if they are fed no more than 2 times a week (recommended). Bettas are alot more likely to get diesases from live worms. I somewhat doubt it was the FDBW. It isn't really a 'worm' at all. It is misquito larvae.
"what do I look for when choosing a new betta?" Well, are you trying to rescue the really sick ones or are you trying to get a (relatively) healthy one? For the first, it is easy to tell when a betta is sick (most times). Second, if you want a healthy one, those are the ones that will have alot of energy. They will generally be a little smaller than some, but they wont look like they are starving. Inspect the face, gills, fins, and body for ich, fungus, bacterial infections, hemoraging, cottony patches, flexibactor, pop-eye, etc.
To clean and sanitize a tank, I would just run it under hot water for a while (unless the tank is plastic!). After the hot water, it is a good idea to leave it outside for afew hours, if you have access (and your neiboor's dog wont eat it). After that, I think it is Ok, but if anyone else on the thread has another suggestion, please suggest it!
Good luck with your next rescue!