What type of spider did I find?

The black structures were pedipalps. This is where male spiders store sperm to transfer to females. Mating is very dangerous for male spiders so the pedipalps minimize body contact to a minimum. Most males fill their pedipalps and then leave their webs, wandering in search for females. They court the females by pulling the strands of their webs. The female recognizes the frequency of the vibration and this saves the male from being mistaken for a trapped food item. Some male spiders wrap food items to present to females. This distracts the female long enough to allow the male to transfer sperm. Males are almost always smaller than females and have longer legs. Another strategy is for the male to be so small the female does not recognize him as prey. Several males will live in the web of a large female and mate while she eats. They may also consume some of the female's food. The black widow often consumes her mate after mating, but his pedipalps break off in her genital opening, preventing any other male from mating with her. This means all the widow's offspring will also be the males as well. What you saw in your basement were probably wandering male wolf spiders. They are large but harmless and carry no venom. The female wraps her eggs in silk after laying them and carrys it around with her. Wolf spiders don't build webs and when the babies hatch, they ride on the mother's back for a short time. Fishing spiders can also be rather large. The female builds a web over shallow water and actually catches small fish.