How sweet that you will be opening your home to another fur kid! And, best of all, you are looking to adopt a shelter kitty. Kitties may act like they are the only ones that exist, but secretly they really enjoy each other's company :smile:
While URIs can be common in shelter environments, I have never had a problem bringing a shelter kitty into our home...we have 7 and they are all shelter rescues. The only concern would be if Debbie has an immune-compromised disorder. Otherwise, you would just want to take you new kitty straight to the vets after adoption for a thorough checkup...they can let you know if s/he needs any meds.
As Debbie is 13, I would recommend an adult (6 or 7+) for a couple of reasons. First, kittens and teens usually have waaaaay too much energy for an older adult, something that could cause resentment. Second, you will pretty well be able to see the 'purrsonality' that your new housemate will have. As you already have another cat, you are looking for someone who gets along with the other kitties at the shelter...not necessarily fawning over them but very okay when others are around. And since Debbie is queen, it is easier to spot a non-alpha adult...because all kittens are crazy little balls of energy! Finally, older cats are not adopted nearly as often and many will have to live their lives in a shelter environment (if they are lucky enough to be at a no-kill). Give a more seasoned girl or guy a forever home!
Also, don't forget that it's very normal for cats to take a good month to get used to having each other around...hissing and a general level of 'I hate you' can be normal at first.
And, since you have had a DK, have you considered adopting a special needs? Most of ours are, and most do NOT require anything special (one has an amputation, one had a mild heart condition that has since resolved, two had severe dental issues that were taken care of, and we've had behavioral issues that really required nothing more than a willingness on our part to get to the root of the problem...everyone is great today!). Oh, and our DK!
As someone who has spent MANY years in the rescue world, I find that older and/or special kitties have more than enough love to give. :RAHCAT
Congratulations on your decision to adopt!