Tell us where to go...

Looks like you've bought something without deciding what you want to use it for.
"I am completely in the dark about what to expect from Britrail passes and their routes". Reckon ona any town over 50,000 population having a railway station, and many smaller ones as well. Places like Chatsworth House or Balmoral are in the country, not in a town or village, so getting to them by public transport is difficult, you may need a car.
To answer your question, click here for a map of the rail network (all routes). You will notice boxes around the big cities. Outside these boxes all stations are shown, inside these boxes they are not, you need to use more detailed maps.

Now, you have to decide what sort of things you want to see, and where to visit. That is a matter of personal taste. Apart from London, Bath is popular, York, Edinburgh, a whole counry in fact, just choose.
Once you have decided what to visit and in which order, for train times go here: http://www.nationalrail.co.uk/

There is also a book available called "Britain by Britrail" . I don't know if there is a 2015 edition. It includes tourist info on locations available by rail. It was available on Amazon. I read it as a library copy.

Balmoral Castle is only scheduled to be open to the public from April through August 2. Visiting countryside homes such as Chatsworth (near Darby and Sheffield), Blenheim Palace (near Oxford), or Castle Howard (near York) all require a bus connection for the last leg, unless you have a car. See http://www.chatsworth.org/plan-your-visit/finding-us and similar info on each house's web site or see practical info in Rick Steves' guidebook for England or Great Britain (cities covered don't entirely overlap between these books). With 4 months to plan, a guidebook is your best one-stop resource for sightseeing advice, practical details, and transportation summaries to the destinations covered.

If you visit Edinburgh, you might want 3 nights there and two full days for sightseeing. With 6 days total, you could only choose 1 or 2 other overnight stops. York is certainly an easy one, along the main train line from London to Edinburgh. Bath is a detour from that route, usually adding another connection.

You could make one stop along the way, York.

York is on the route directly from London to Edinburgh. York has one of the most magnificent cathedrals in England, York Minster, well worth seeing. York also has a medieval city wall which you can walk along. It has a museum which tells the story of the ancient Roman fort/city that used to be there, and the Viking occupation of York. The National Railway Museum is there. Don't know how much of this interests you.

You also mentioned Bath. Bath is best done as a day trip from London, unless you are traveling directly through it on the way to somewhere else. No, you will not pass near Bath when you train from London to Edinburgh, traveling north. It is a good distance to the west of London.

No, Liverpool is not on the way, either, from London to Edinburgh. It is on the western coast of England, quite a distance north of Bath.

Get a good guidebook of Great Britain with a good map and study it. Then you will be able to formulate a plan.

"We'd like to get to somewhere in Scotland...."

If Scotland is a priority for you, you could do a loop by train through Scotland after Edinburgh, and return down the west coast of England. Post a question on the Scotland Forum if this appeals to you. Several of the regular posters on this Forum are experts on Scotland travel.

Thank you one and all. And yes to the first answer, we scheduled without any big plan. We've been to London twice since November of 2013 - a lifelong dream of mine - and I can't seem to get enough of England. My husband thinks I must have lived there in a prior life. And, since we don't fly, ever, we have to rely on the ship's that cross back and forth. They can't be months apart, only weeks because we have a dog sitter that's charging by the day. The only back and forth I know of is the Queen Mary, meeting this criteria in September (and May, but that's not good for us) I wish there were more crossings to choose from, but just as long as I get to London I'll be able to rest easier. I will get the Britrail book. We are getting our passes here and want to go as many places as we're able. I like the loop of Scotland; that sounds wonderful. If only my husband would agree to move to England....

The most important websites you need to plan such a trip are:> www.nationalrail.co.uk & http://www.traveline.info

On the National Rail website, you need to check the walk on fares for 'today' (so do it early to allow for time difference) & 'tomorrow' - but bear in mind that on Sundays, trains may well be less frequent & engineering work often causes disruption. Saturdays are also different as the fares are cheaper at peak times due to a lack of commuters. Buying 'Advance' fares can be cheaper but ties you down to specific trains. You then need to compare the cost of buying tickets v the daily rate of a Britrail pass. (No point in blowing a day of Britrail pass for a lower cost point to point ticket).

The Traveline website is useful for buses/ferries.

I would suggest the following route (with number of nights in a hotel in brackets). Google place names for more info.
Southampton to SALISBURY (1). Having checked into hotel, take shuttle bus to Stonehenge. Then, back to Salisbury to see Cathedral.

Salisbury > BATH (1). Bath > CARDIFF (2) Visit http://www.museumwales.ac.uk/stfagans/ by local bus. Also visit Caerphilly Castle (7 miles N of Cardiff). See Cardiff Castle & Cardiff Bay.

Cardiff > PORTHMADOG (2). Visit Portmeirion. On leaving Porthmadog, use the Welsh Highland Railway to Carnarvon (Castle) . See -http://www.festrail.co.uk; Then bus to Bangor for train to CONWAY (1) - see Castle & maybe visit Llandudno.

Leave Wales by train from Conway/Conwy for Chester - have a walk around this English border city before taking train to WINDERMERE (2) in the Lake District.

Windermere > to Scotland? or return south to London?

If going to Scotland, the West Highland Line going N from Glasgow to Fort William & on to Mallaig is very scenic. From Mallaig, you can go by ferry to the Isle of Skye & then bus across the island to Kyle of Lochalsh to get back to another scenic train line that will get you back to Inverness from where you can reach Edinburgh. Alternatively, bus from Fort William to Inverness. (Note that this is quite a long trip & you would have to work out where to stay).

If going from Edinburgh to London, it is well worth breaking the journey with 1 night in York.

So, that is an idea of a doable route. Do further research & make any changes that you think would be right for you. (You could, for example, go straight from Bath to Winderemere and cut out Wales or not continue north to Scotland).

You may also consider setting up a base and staying in one place for longer as the continual moving from one hotel to another may not be for you.

www.visitengland.com
www.visitwales.co.uk
www.visitscotland.com

We are doing a similar trip this year, although for a longer period (we are seniors as well). We will cross on the QM2 in August and return on the westbound cruise 20-27 September. Is this your return cruise as well? We will be renting a car in England as we are comfortable with driving there. Last year we did take the train from London to Edinburgh (a great trip). We highly recommend Edinburgh and recommend at least 3 nights (2 days) there. Let us know if you will be on the QM2 with us and maybe we can meet.