Seat61.com will set you right regarding the QM2. Bear in mind, if you want to try something closer to the reality of everyday shipping, there are a number of specialised travel agencies who can liaise with freighter companies and sell you passage in the surplus crew cabins of container ships. If you choose to go one way by boat and the other by plane, you might prefer to travel to the UK by sea and back by air, because almost all eastbound flights travel overnight, which is much less comfortable IMHO.
For all your rail travel in the UK,
National Rail will give you train times and fares. These
maps may also give you some inspiration, and if you're going to be based in London, specifically
this one of both the London Underground and all rail services.
Enjoyable day trips from London are numerous - Oxford, Cambridge, Brighton, Salisbury and (a bit further out) Norwich and York are all (for instance) each easily visited in a day trip. Remember that there are three basic grades of tickets on National Rail (in increasing order of price): Advance (buy in advance from ~ 12 weeks ahead, but use only on the specified train), Off-Peak (buy anytime, travel outside specific rush hours) and Anytime (buy anytime, travel anytime). Some train operators on heavily used commuter routes don't sell Advance tickets. To get the cheapest Advance fares before they sell out (just like Amtrak buckets) watch the
National Rail Booking Horizons page which tells you company by company when Advance fares become available (they normally update on Fridays).
You can buy tickets at any station, or online from various websites. Thetrainline.com is the one with the biggest advertising budget, but they charge unavoidable booking fees for the same fares you could buy elsewhere without a charge. For Advance train tickets, I prefer the website of
East Coast.
Feel free to come back with any specific questions and I'll try to help.
RailForums may also be worth joining / reading; the closest equivalent to this forum in the UK.