At the American Muscle Car Museum, we maintain the entire collection to where each car is kept in driving condition to preserve the collection and the value of the cars. Each car is annually brought out to the maintenance shop, inspected before starting, and any adjustments, repairs, or fluid changes are made. Then the vehicle will be started, ran, and brought up to temperature. We are fortunate to have the museum's grounds located on 42 acres which allows us to put "miles" on the cars in a controlled setting. After being brought to temp, each car is allowed to cool down and be re-inspected. We have a master inventory list and an inspection checklist for each car.
We deal with many issues with older cars with the three main significant items: fuel, coolant, and batteries. On the fuel, for any of the cars 1982 and older, we use Sunoco 110 Octane Race Fuel and keep 3-5 gallons in each car. Along with using this high-grade fuel, we add STA-BIL 360 fuel additive. On all cars 1983 and newer, we use Sunoco 93 Octane Non-Ethanol Fuel, also with the STA-BIL additive. On these newer cars, we keep 1/2 a tank of fuel in them because, on most, the fuel pump is located internally in the fuel tank. For coolant, we use Evans Waterless Coolant and CTEK Battery Chargers and Maintainers for the batteries. 
We have a detailing schedule for each car, using Rupes Polishers and detailing products combining auto geek and 303 products.
As far as parts and supplies for these cars, we have developed many good relationships and sources over time.  
Two people Currently maintain the collection. Ed Dedick And Ryan Colin.  Jerry Frye retired in 2021.  Along with maintaining the collection from a mechanical running and preservation of all the cars and memorabilia, we also ensure an extensive photo set for documentation and historical reference provided by the museum's photographer Andrew Mackey.