Changing ISP is The MAC Process
You choose whether to keep your line rental & calls with BT or switch it to Be. you don't save much with Be, say 80p / month, dependant on plan.
Are you sure you can get Be? Put your phone # in SamKnows: UK Exchange Search
and post the resultant link.
Speed: Post your router stats and we will tell.
An N laptop will work with a G router. You probably won't need better unless you have loads of PCs doing loads of transfers.
1999: Freeserve 48K Dial-Up => 2005: Wanadoo 1 Meg BB => 2007: Orange 2 Meg BB => 2008: Orange 8 Meg LLU BB => 2010: Orange 16 Meg LLU BB