UK FIRST TIME

First time in uk so pretty clueless . I dod check out the visitbritain.com site which is supposed to be the official travel site of UK . would request some feedback on
1) The planned itinerary
2) Using liverpool as our base ( where all to go in north west england – we have 5 days there )
3) Scotland – what to do in 3-4 days ? ( can we cover a few places in the highlands and edinburgh as well ? )
4) Transport – best and cheapest way to get from london to liverpool and also from liverpool to areas nearby – trains are frightfully expensive !
5) No time to plan – we are a month away from the trip – so any help would be sincerely welcomed !
Thanks and happy travels !

DHIR