I agree with the poster above's comments regarding powerline adapters and the flexibility they provide.
I think avoiding the added complexity and cost of a second router or WAP if you can make it work without them is good.
I would try using a pair of powerline adapters to connect from the basement cable entry point, which is where I assume the cable modem will be located, up to the location where you have to have a hardwired connection, and placing the wireless access point and router (if that's not built into the cable modem) there.
If you don't require a hardwired connection on the first or second floor, then I would experiment with placing the wireless access point in various locations using the powerline adapters until you find the place that offers the best coverage or come to the conclusion that a second WAP is required.