You will need either of these cars:
1951 Holden 50-2106 FX UTE - Barn Find
1970 International Scout 800A - Barn Find from Blizzard Mountain for Forza Horizon 3
I found that I had to pick a Class S1 car for Online Adventure, but for Private Online Adventure I only needed to upgrade to Class B. One option is to pick up a second car and upgrade it to a different class. For example if you have both a Class A and Class S Holden FX UTE there is more chance you can join an Online Adventure in one of them.Mr Fiddler
points out that this can be done in Custom Online Adventure, where you can specify the car class.
You must complete all 4 events, joining part way through does not count. Private Online Adventure ensures you and your friend start at event 1.
This is worth the effort as the 1969 Lola #6 Penske Sunoco T70 MKIIIB prize car is an exclusive, and when I checked there weren't any up for auction.