All CMOS devices are potentially ESD sensitive. The size of the package has little to do with just how much so, but semiconductor geometry (feature size) does, which tends to mean that newer parts, which do tend to be in smaller packages, are often a bit more sensitive. Even stuff from the late 80s and early 90s often has quite a few CMOS components which can be sensitive to ESD. Purely TTL boards tend to not be overly ESD sensitive, and you likely don't have to worry.
Do not wrap a board in aluminum foil if it has a battery. You'll potentially short out the battery, which could cause it to leak or even explode! ESD bags are just slightly conductive: enough to dissipate and divert static charge, but not enough to short out powered components.
ESD bags can be bought from most electronics suppliers, but the big names will tend to overcharge you. You'll need a pretty big one for your average JAMMA board, which may be a little harder to find.