4-port wireless routers have 4 wired connections. The 4 does not refer to the wireless part. Connecting 6 computers wirelessly will be possible.
Range is a major issue and it will depend on both the distance between the router and the computer and on what obsticles (walls, floors etc) are in the way. An old house with thick stone walls will obviously be more of a problem than a modern house with plasterboard walls. Choosing a sensible (central) location for the router will help.
One technology which does improve coverage is MIMO (Multiple In Multiple Out). There are a few new routers offering this technology and it does appear to improve coverage considerably. However, being new technology, it does not come cheap. An example of MIMO equipment is the Belkin Pre-N equipment. Although this is a cable modem router it can be linked to an ADSL modem router for use on an ADSL line. Cost for such equipment would be ~£120 for ADSL modem, Wireless router and one wireless card for a computer. Assuming you have one pc connected using a wired link you would then need an additional 4 wireless cards for the other computers. These would cost £60 each.