A wireless modem router (usually) comes with 4 ports so that up to 4 PCs can be connected by cables. Ideal in this case as the desktops are close together. The lappy can then be connected wirelessly via PCMCIA card.
As long as the modem is an ADSL modem/router then any make will work with the BT phoneline.
Most major brands even do 'bundles' of routers and cards sold together.
Stick with the known names, Linksys/Belkin/Netgear etc and you can't go wrong.