Most commonly, users with Cable broadband (where the ISP provides the Cable Modem) use separate modem and router. With ADSL via the phone line, the preferred option is to use a combined Router & ADSL Modem.
"Is it possible to conect my computer directly into the modem and also run the wireless from the router or will need to connect to the router and thus to the network?"
The function of a Router is to allow multiple computers (or other devices) to have simultaneous internet access. A stand alone modem will only allow the connection of a single device - the ISP only allocates a single IP address and every internet connection must have a unique IP address. When a router is used, it gets the single IP address and in turn allocates IP addresses in one of the ranges reserved for Local Area networks, most commonly 192.168.x.x addresses, to the computers connected to it. It then "routes" internet traffic to the appropriate IP address in the LAN.