FWIW, cards can provide drivers via the Declaration ROM, but there is no requirement that they do so. They must have a declaration ROM of some sort (otherwise the card isn't mapped into the processor's address space), but they do not need to provide a driver.
Graphic cards almost universally do, otherwise you couldn't really boot with them (there wouldn't be any display output until after booting far enough to load the driver, and then even then only if the driver is properly installed and you're not booting with extensions disabled).
Apple ethernet cards do not have drivers in the declaration rom (or system rom for onboard ethernet), you need the drivers in the extensions folder. The Asante cards also do not have drivers, they pretend to be Apple cards and use the Apple drivers. The EtherPortII cards actually do have a driver in ROM, which makes things pretty handy when using that card.
SCSI cards virtually all have their own drivers in ROM as well, since that's how they boot. When the slot is selected in PRAM, the system ROM uses the drivers in the declaration ROM to "boot". I put boot in quotes there, since different cards do different things from their drivers, most commonly they pass the boot sequence through to the driver loaded from the selected disk's driver partition.
Other types of cards are hit and miss.
As for what you "should" do, it seems like lots of people have lots of opinions for you to choose from. I've already gone through the "omg, must fill all slots with coolest stuff!" phase, and after accumulating a box full of neato nubus cards, I found I didn't really use most of them. While being neato, their primary function seemed to be converting electricity into heat. As far as graphics go, the speed difference between low end cards and high end cards is largely lost in the rounding error of the last 20 years of technological advancements. The onboard graphics will do 1152x870@16bit just fine with appropriate vram. If you need higher resolution or more colors, get a card.
