Welcome & Congrats!
Welcome to the forums and congratulations on your Airstream!
I think you are wise to check out the safety issues first. Brakes, tires, lights... primary importance. Next try out the inside be sure nothing is leaking... if your trailer is "usable" (even in your driveway) I would "camp" in it for a weekend and see what works, what doesn't, how it feels... what is needed. By the end of a couple of days in your 'stream you will know what is next after the safety items.
If the tires look good but are more than 5 or 10 years old and have been sitting in one place, replace them. They aren't as strong as they look.
We are eager to see pictures of your Airstream, both inside and out! Now and later! Post away!
Mrs. NorCal Bambi (traveling in S Tardis)