By "Number Cards" I think you mean "Parts Trees" or "Sprues".. They're also known as "Runners", although one doesn't hear that term often..
If you can't see ALL of the part AND get a brush to it easily after it's assembled, paint it before you assemble it... And you don't need to prime anything but metal, with the exception of metallic finishes... Sometimes you don't have to do that, as when you're finishing an aircraft that's actually painted with aluminum paint..
Working in sub-assemblies is always the best approach with tanks and other AFVs, and with most aircraft...
I don't paint parts "on the sprue" except for parts that can get a quick shot of spray Zinc Chromate primers, or aluminum, or RLM grey (whatever's called for) for the base-color. For instance, when doing aircraft, I like to to shoot the interiors of the fuselage, gear-bays, bomb-bays, and cockpit floors and bulkheads in one step...
As for doing washes, I generally do those after the parts are in the sub-assembly, but don't stop there.. You need to combines washes with dry-brushing... Washes add depth to details, dry-brushing is for high-lighting them.. Use the two techniques together on interior parts.... Base-color, then detail-painting, then wash, then drybrush...
Painting some parts on the trees is ok though, especially if they're small and a different color than the part they get attached to... I generally cut the part from the tree, leaving a bit of sprue on either side of the part for a handle... There's no law that says you have to keep your sprues in one piece, lol.. But, if you do, make sure you either leave the number tag on the sprue section you cut out, or write it on the part or sprue with a Sharpie or something similar, if there are "Left and Right" versions of the same parts... You WILL forget...
One major exception to removing parts and then painting them? Tank and AFV roadwheels... I leave those on the sprues and shoot 'em with the base color befre I even start assembly.. I'll touch them up with a brush later, when I sand the mold seams and paint the rubber portions...