Congrats on your purchase. I wholeheartedly agree with previous posts and strongly encourage you to consider axle replacement before much use.
Put me in the "true believer" category when it comes to axles. I never did replace them on my '72 Overlander before I sold it, but did replace them on my '73 Sovereign
this spring. WHAT A DIFFERENCE! It rides so much better! Here is a good Before/After comparison
Not only does it restore the suspension your Airstream was designed to enjoy (protecting your investment (shell/floor/frame/interior) from excessive vibration), it also provides brand new brakes and bearings, and peace of mind knowing your 6000 lb is operationally safe to tow. New tires would definitely be on my list as well, unless they're less than 3 years old.
A wheel coming off or tire blowout will easily cause more damage to the skin/wheel well than the cost of new axles or tires.
Sounds excessive, I know, especially for a newbie. But your axles are SHOT (especially from the streetside pic) and are providing no cushion at all IMHO. New axles aren't necessary if you plan to keep it in your driveway, but if you plan to travel much, I'd suck it up and do it. You'll be glad you did.
A set of Dexters can most likely be ordered locally for less than $1000 with NeverLube hubs and shock mounts and installed with little more effort than OEM, at least according to my experience. PM me if you have any questions regarding details.
Good luck on restoration. It's lots of fun!