It might be useful to see how the current battery is connected, and make sure to install the new one the same way (by default, should be 12v negative ground for the 1956).
For the general maintenance, most of the necessary information can be found in the Owner's manual:
https://packardinfo.com/xoops/html/downloads/56_Pack_OM.pdf and especially page 26. Since this car is new, to you, it would probably make sense to have it closely inspected to make sure that everything is sound mechanically, etc., and it is safe to operate (especially the brakes).
For the regular maintenance, you should be able to use the materials available at the local auto-parts stores.
Oil - viscosity/type according to the manual; I would use synthetic (although, some people are against it).
Oil filter - you need to find a cartridge that fits. If the local store does not have them, you should be able to order a bunch of these online.
Fuel filter - same thing. Original filter is a cartridge in a fancy glass bowl. For a quick temporary fix, however, you can use a generic in-line fuel filter of applicable size.
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