Just wondered if a broadband modem, an access point and a notebook
with a wireless network card is enough (hardware wise) to get online
wirelessly.
In theory yes, but in practice I don't know, suspect
complications with unknown devices and their configuration,
which is unlikey to be one the average person is familiar
with.
If yes, what kind of cable should I use between the access point and
the modem (a “router to client cable” or a “peer-to-peer” cable)?
A standard network cable. I suppose you could call that a
"router to client cable" but nobody does, there are only two
common cables used on this consumer equpiment, standard or
crossover. You don't need a crossover cable.
Can I later add more wireless clients to the network without
problems?
No, and that is why most people would get a router, not use
an access point, since a wireless router will replace the
access point. You could instead keep the access point and
add a router too, have both pieces of gear.
Having both pieces of gear is redundant, can be a waste of
gear and $ if you didn't own the access point yet, but it
has an advantage as well- by having the access point
installed remotely, a good distance from a wireless router
you would expand your wireless coverage area.
Can the AP hand out ip adresses just like a router can?
No, the router does that. The router can do it THROUGH the
access point if you had both but the access point alone
doesn't function as a DHCP server. Some modems now do this
though, are more than just their product description of
"modem" would imply once you read their product
descriptions.
In general though, if you don't have the gear yet, buy a
wireless router.
