What are the health risks a dog in a shelter runs & for which I’ll have to check before bringing the dog home

I know nothing about dog diseases, I guess like cats, they’ll have certain vaccins and deworming every 6 months?
I’m going to the animal shelter tomorrow and I need to make sure I don’t end up with a dog who has health problems, for 2 reasons: obviously it means more money spending on vets and also, it’s heart breaking to have a pet who’s sick.
Is there a virus he could have? I have a cat at home so I don’t want to risk any contagious infection. Please help!

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