Certainly not cheap but Kingston, PNY, Integral and Sandisk are all fine.
Regarding size it is up to you as to what you want to store on it as to the size needed.
Mine are all 1 or 2GB and only used for software transfers between computers that are not networked. So i don't know how good they are at long term storage.
regarding your old HD, I have a 250GB external HD that has all my backups on and is then shutdown, never left running like the PCs.
I just backup to it every week and sometimes run a AV scan and run MBAM over itthen a quick defrag if I have transfered a lot of stuff and shut it down. If any hard drive is going to pack in, either on the computers or on the external HD all I would lose is the last weeks work because backups are duplicates up to last Saturday.
You should never put everything onto an external HD and then delete it from you computer, you are left with only one copy.
dave