Novice : how to stretch wireless network?

["Ou Phrontis" <OuPhrontis@gmail.com>]

Hi,

My neighbour and I are sharing his cable connection.
Trying to get a better wireless coverage on my end
of the bargain.

So far he has a linksys wireless router which my debian 3.1 machine
is connecting to.

I have a spare linksys BEFW11S4,  which I want to use so
the whole house has wireless coverage.

My idea.

I put my linux machine as close to the neighbours router
to get the best possible signal, then using a regular
ethernet 10/100 card run a cable to my wireless router.

I would like everything to be as dynamic as possible.
My linux machine is picking up all the information
it needs from the neighbours router to get to the outside
world.  So I need to pass this information on.

So I am thinking I'll run a dhcp server on my linux box
and then gateway software??

Then which port would I connect to on my router?
WAN, uplink, regular port.
Will I be able to get the router to pick up the
information dynamically from the linux box?

Answers, suggestions, good links  all greatly appreciated.

Thanks in advance.