If you had the option I would run the computer that is going to used the most via hardwire (ethernet).. You are going to get higher speeds than you would wirelessly.. You should be able to do this.. most of the router have a 4 port switch...
As far as running new cable.. that is a possibility.. however, you can not run data, internet, and voice on the same line.. so you would have to run cat3, phone cable, and cat 5 or cat 5e for internet.. So the best way to go would be to use the wireless.... There are other options such as over power... which uses your houses power lines to create a network.. I have never used it but it is an option.
As far a wireless goes.. it can be as secure as you want it to be.. you can filter mac address, limit the number of ips that the dhcp releases, hide the ssid, and of course encryption. Always make sure that you are using the highest encryption that you can get... WPA is better than WEP.. and 128 bit WEP is better than 64bit...