Some of the past banners I've made for sites (or even just for fun) for the site itself, I've used 700x300, 982x250, 851x315, 700x110, and 750x325. I actually prefer the longer, but wider sizing and would honestly probably go with that if it fit with the site if I were to make one these days. Would probably depend on the site though since, of course, I'd want to make something that fits it.
For signature ads, I always did standard signature image sizes, so usually somewhere in the 300-400 range for width and the 100-200 range for height. For affiliate images, I always did 88x33 and never deviated from it. I never really did anything outside of signature ads and affiliate buttons, so I'd probably stick with those sizes even today, but I would probably also strive to have a few different options in terms of style and sizing to allow people to choose what they want while also not compromising on branding. If I need something super specific, like a 400x400 image for ad space for example, I'd probably make it when I needed it, but keep it available somewhere on the forum (probably the staff boards) in case it was ever needed again.