>Would it be plausible?
Armor is maintained and operated in the middle of combat zones…it's plausible.
>Would it be plausible to maintain a modern tank after the collapse of society? Or would an old museum piece be a better choice?
A "modern" tank, which would be the M1 (or similar platform like the Leo 2, Chally 2, ect…) is going to be far too difficult to maintain and operate. They rely on extensive and well supplied logistical systems, most of their systems are very advanced and difficult to repair/replace such as the Fire Control System, Powerplant (engine), Navigational Systems, ect… The "Pros" you do have are far outweighed by the "Cons".
Additionally, you have to being into consideration Training and Familiarization (Fire Control System, Driving, Radio Systems, ect….), Tank Gunnery (the maingun and coax), Vehicle Maintenance (including electronic, track, engine, ect…)
Some of this can be tackled through obtaining manuals, but you'll need someone with experienced on armor to help you to train and become familiar. You need a 19K, preferably a Master Gunner.
Once you've accounted for the above; this is where you measure the hardware "Pros" and "Cons".
Something like the M5 Stuart as in your photo will run on simple Gasoline (Petrol), uses a 7250HP 7-Cylinder, Radial engine, 1/2-2in of armed plate, and is armed with a 37mm Gun and 3 M1919A4s.
Pros of the M5:
- Lightweight, meaning it's fast.
- Wide track placement, superb in muddy operationing conditions
- Gas, which simplifies logistics
- Simply 7 cylinder radial engine, easily worked on
Cons of the M5:
- It's weight is a detriment in certain environmental conditions (e.a. Winter), it doesn't have the mass to prevent slippage or sliding.
- Thin armor, easily penetrated by larger caliber rifles
- 37mm ammunition has NOT been produced in over 50 years, assuming the M6 Gun is still operational. Some stockpiles may still remain. It's also limited in a penetrating power, it was designed as an AT round during World War One.
-M191A4s are available, but not overly common, but linked .30-06 (7.62x63mm) isn't common…at all. You'd have to find M1 links or manufacture Canvas belts and obtain surplus .30-06, current production civil .30-06 is too "hot" for legacy weapons.
- The engine is over 75-50 years old and utilized parts that haven't been mass produced in over 50 years. Parts would have to be sources from stockpiles or fabricated
- Gas (Petrol) is the most difficult fuel type to refine
However, not all armored vehicles are equal. An M5 might not meet the cut, but an M4 may. Personally, I'd shoot for an M48 or M60. Both are no longer in active inventory and are in museums all over the place., yet still meet the demands of the modern battlefield.
With an M48A3/A5 or M60A1/A3, your have a much more powerful engine that is still in use, the 750HP Continental AVDS-1790-2 V12, the M41 90mm maingun or M68 105mm maingun, plus 90mm or 105mm ammunition for the maingun, 7.62x51mm for the M73 Coax, and 12x7mm (.50cal) for the M2HB are all still in Active Military Inventory, armor is 4 inches on the M48 and 6 inches of the M60 more than enough to defeat anything up to 90mm and defeat legacy AT weapons like the RPG-4 and M72 LAW.
You're not just limited to the M48 and M60, any Post-Second World War armor is applicable, such as the M26, M41, M46, M47, M103, ect… all will be armed with at least a 90mm, have at least 4 inches of armor and have an engine over 400HP.