Choosing an Adult Dog
If you are going the adult route there is an advantage: you get what you mostly see. The dog has bloomed already and you are more likely to have a transparent idea of what he is rather than a blank slate. While this is a good thing, should there be a behavioral problem, by now it has put roots, and therefore it is more difficult to eradicate.
Upon selecting an adult Rottweiler avoid shy or aggressive Rottweilers, as they may be a handful for inexperienced owners. Spend time with the Rottweiler, walk him, and ask him some commands. Have a feel of who this Rottweiler is and what he or she has to offer. Ask the shelter or foster as many questions as possible. If you are unsure, most will be happy to allow you do give the Rottweiler a try so you can have a better feel. If you have other pets at home, this trial period will allow you to have an idea if there are chances of everyone getting along.
If you notice any problems, honestly think it over and discuss options with the shelter/foster parents. Many issues can be reduced and even solved with the aid of an experienced trainer or a reputable dog behaviorist.