Without actually seeing what BT cable points are in the house already its difficult to say for sure...
If you are having a BT phone line activated then it will usually include a engineer visit and they will within a reasonable set of rules locate the master socket at place you ask, though things like running it from the hallway up the stairs and into a room upstairs may stretch things. Having some CAT5e Ethernet cable in place with the spare length as suggested will often mean they will happily use that.
On the distance is everything and you don't want a lot of cabling, while true, the effect of 5 to 10m of good cable that rather than cheap aluminium (and if buying CAT5E ensure it is copper and not CCA) is minimal, unless you are going to worry about getting 36 Mbps rather than 37.5 Mbps. On the interference aspect so long as twisted pair cabling is used some proximity to mains wiring where it cannot be avoided should be OK too, i.e. best practice has been quoted at you.
A single run of cat5E will carry both the phone and broadband and you can then split them out using the usual connectors/filters at the final destination and is better than running a 'broadband' and a 'phone' cable.
Ignore all the coax cable and Virgin Media stuff the Openreach installers won't touch it.