Depends on where you locate the router. Preferably central position. If you are talking about a mutiple storeys house, you might need a bridge or repeater to broadcast the signal, otherwise the signal is generally strong enough for an apartment.
For normal internet usage, a 802.11b standard is good enough, however, the price gap between the 'b' & 'g' is narrowing, so if I have excess budget, I would go for a 'g' standard.
As for security, I do not know about other brands of router, for mine, I could set a 128 bit WEP encryption as well as limit the access by IP address and/or MAC address, that is, to fix the IP for each of your PC and notebooks, and only the PCs with these authorized IPs and/or MAC addresses are allowed to log into your network.
Depending on models, you might be disable the DHCP server feature of the router, so that it will not give out an IP address to any computers nearby with a wireless NIC on. Alternatively, you can also limit the IP range to so narrow that only a limited number of devices can be attached to your network.
Other security measure would include not to broadcast your SSID so that others could not detect your network.
Please be very careful and write down all the passwords and IP addresses especially the 128 bit encrypted password. You do not want to be locked out from you own network accidentally.
Best regards