Using WAPs with routers and hubs

I'm looking to setup an integrated wireless/wired network and am a
little confused on if I need an access point or if I can use a
wireless router to do what I need to do. My projected setup is as
follows:

Cable modem to a hard wired 4 port router. One computer will attach to
this router on a seperate ip address. There will then be a hardwire to
an access point(?) that will be located on a different floor and that
will house a seperate network. (I figure putting the access point on
the seperate floor will help with connectivity as I'm dealing with
concrete floors)

On the second floor I will have, as stated above, the one access point
at the drop site and then a second access point (or should it be a
wireless router) where the computers will be located. The access point
will then connect to a 10 port hub that I already own and the
computers will attach to the hub to connect the second network.

I understand that my hard wired router will act as the dhcp server and
that my access points or routers should have dhcp turned off. But my
one question is for the computers attached to the hub, will they be
able to get their ips from the router via the access points (suspect
the answer is yet) and since the whole wireless connection is for
internet connectivity there should be no problem with the NAT
functionality of the router running through the access points and the
hub, right?

As you can see I have some of the basics but am a little confused on
the finer points. Any help, suggestions, recommendations on hardware,
etc. would be GREATLY appreciated.

Thanks & Cheers
Mike