What hardware upgrade would be most beneficial for a Mac? Would it make more sense to buy a Mac with a better processor, or with a better graphics card, or a SSD?

For general computer use, mainly word processing and Chrome/Safari.
My suggestion is to always take the second fast processor available and invest the rest of your budget in RAM. The fastest processor is usually too expensive. You don't get much more speed for the price difference between the fastest and second fast.

And don't upgrade the RAM in the Apple Store. Find a local reseller, who delivers your System readily build with non-apple brand RAM with warranty. You could get twice the RAM for the same price. But never ever use discount RAM. It's not worth the hassle. 

EDIT Oct 12:

bmike's comment is right. The SSD is right now the single most important component for your Mac's speed.

So take the SSD. Even if you can then only afford the slowest processor.

BTW. Are there still Mac models w/o SSD?