Question one: what hardware and software will I require to connect three clients based from home (at home end)?
It depends on the link you are planning and estimate of the cost.
Link : Async or ISDN or Leased line
Hardware : Based on the link you should select the Cisco Routers. For async link modem is sufficient, routers not needed
Software : Cisco routers bundles with IOS.
Question two: what hardware and software will I require to connect three clients based from office to home (at office end)?
Link : Async or ISDN or Leased line
Hardware : Cisco routers (Access routers)
Software : Cisco routers bundles with IOS.
Question three: will I need things like phone lines if so then what type?
You need links to interconnect between cities. Links can be of Async or ISDN or leased line. According to your cost estimate you can select any one. All these variety of links are provided by telephone companies.
Question four: what should be the ip configurations; what protocols will I need to use?
refer the link http://www.cisco.com/tac according to the type of link , you can see sample configuration after you select the model of Router in Hardware support.
Protocol : IP