If you have the option, it might be wise to buy your house appliances in Lebanon. The prices are usually a bit lower than in US and Europe. There are several big department stores as well as home appliance stores where you can find whatever you need. If you are in it for a bargain there are certain areas in the bigger cities that will sell goods of a bit lower quality, but much cheaper. If you're in Beirut, try your luck at the smaller stores around Dora and Ouzaei.
To get access to internet in your own home you can either apply for DSL/ADSL broadband connection, for which you will need to have a phone or DSL landline or you can contact your local neighborhood internet provider and he will simply hook you up to the server connection in your building through your own modem. There is also the option of portable wireless internet through one of several commercial providers.
Using a phone in Lebanon is expensive and sometimes very annoying. The lines are not well maintained and especially international phone calls are not cheap at all as well as malfunctioning.