Current digital models, i.e. SB-700 & 910 are backwards compatible with the F100,
This part is right. The SB-24 is a great flash, but is older, and a short a couple of later features (3D, Auto FP). The Nikon link above suggests the SB-27 for the F-100, but the F-100 manual (flash section) covers several from SB-24 to SB-80.however you can save some money and find a used SB-24, 25 or 28 for cheap.
When you say it will "work", does that mean I can put the sb 700 on the hotshoe of the f100 and put it in manual mode and it will fire?