traveling to ireland, england and europe this fall

I've never had any trouble obtaining train tickets at the last minute. There may be local exceptions, perhaps commuter trains at rush hour here and there.

You shouldn't have to take a bus to Liverpool. This link from the Man in Seat 61 will cover all your sail-rail options -- https://www.seat61.com/Ireland.htm#.VfXUQn0pDMJ

If your main focus of interest in England is getting quickly to southeastern England, you would be better off taking the train from Liverpool to SE and picking up a car there. If you took the train from Liverpool into London, you could take the train to Gatwick Airport, pick up a car there. This would put you well south of the London traffic and close to the south coast.

To the east of Gatwick Airport is the county of Kent with many lovely castles. Some are out in the countryside and better reached by car. However, they can be reached by train from London, with either a short walk at the end of your journey, or a short taxi ride from the train station. Farther east, Canterbury may be one of your destinations on your list. It is easily reached from London by train.

Obtaining train tickets at the last minute on local trains can be expensive, as the cheapest way to buy tickets is weeks or days before. To cut your cost for walk-up tickets, get a senior railcard, which cuts the fare by approximately one third. It helps a little on the cost if you can also buy your ticket a couple of days in advance. You will need a passport size photo of yourself to present when purchasing the rail card at a station. They will attach this to your rail card.

From the National Rail website:
Save 1/3 on most rail fares throughout Great Britain with a Senior Railcard. With a Senior Railcard anyone 60 years or over can save 1/3 on all Standard and First Class, Anytime, Off-Peak and Advance fares for £30. Take a look at all the ticket types you can make savings on with a Senior Railcard.
http://www.nationalrail.co.uk/times_fares/pr7bb7e80a040002001b255638df2424.aspx

Where to buy:
At a Staffed Station Ticket Office. You can buy a Senior Railcard at any staffed station ticket office or National Rail-licensed Travel Agent. The main advantage of this is that you can do it on the day you are traveling. You can buy online or by phone.
http://www.senior-railcard.co.uk/using-your-railcard/where-to-buy/

You can also buy rail cards online:
http://www.nationalrail.co.uk/times_fares/46540.aspx

Pay close attention to the restrictions:http://www.senior-railcard.co.uk/
Please note: Railcard discounts are not available on tickets for morning peak period services, for journeys wholly within the London & South East area on Monday to Friday, except on public holidays. See Time Restrictions for further details.
http://www.senior-railcard.co.uk/using-your-railcard/travel-times-tickets/?nreTrack=seniorrailcard
http://www.network-railcard.co.uk/clientfiles/files/Map.pdf?_ga=2.66467054.173281282.1496942447-748198787.1496942447

Consider taking the bus (coach) if you will be traveling from one town to another in southeastern England. The bus (coach) is cheaper than the train. For long distances it is cheaper than the train, but can take a very long time. For short distances, much better, if you are just hopping to the next town over.

take the Eurostar to Calais France. Then travel by train to Budapest.

Snulli, you need to do some research about how the rail system works if you want to use it at the last minute. I recommend the following website: https://seat61.com/
You need to get some idea of the geography and main routes.
For example, taking the Eurostar to France, Calais is not a good place to get off. It only has one Eurostar train a day, and no onward connections. You need to get off in Lille, Paris or Brussels. Paris and Brussels are major rail hubs, and Paris is a good place to spend time (obviously!). Eurostar tickets are a lot cheaper bought in advance, London to Paris varies between £44 and £191, the only people who buy on the day are businessman on expenses. See the Eurostar website: http://www.eurostar.com

Long distance trains are (in most cases, it varies by rail company) cheaper if bought in advance. Local trains it usually doesn't make a difference. You will almost always be able to get a ticket at the station on the day. Train journeys are often made at short notice. You suddenly need / want to go somewhere today or tomorrow, you just go down the station and buy a ticket, but for long distance it could be expensive.

There is an insurance surcharge for drivers over 70 that rent in Ireland. Also, you are required to purchase the extended insurance coverage.
I assume that you are from North America.
Have you driven in Ireland or the UK.
I have and recommend that you rent an automatic with a navigation system. Having the Nav system was key to not being distracted while driving. Since, driving on the left is different, you don't want to be distracted.

We are planning four weeks driving in Wales and England this October and I planned our entire trip, B &B s, where to park (that is a huge issue in cities) and what to see.

Have you been to the Cotswolds? If not consider going there. The SE is nice, but avoid the M25 parking lot.

If you are using local trains, last minute tickets are fine, but for long distances or sleeper you should consider advance reservations. Do you have a cell phone (mobile phone in UK) that works in Europe?

Plan on where to do laundry, hotels charge a fortune. Launderettes are what laundromats are called in the UK.

If you want to go to SE England, why not fly to London Gatwick instead of taking the ferry?

There is plenty to see in SE England, but it's difficult to advise, as you haven't given any indication of your interests, exactly when you are visiting or for how long. I would recommend in no particular order - Whitstable, Canterbury, Dover, Sandwich, Leeds/Hever/Chiddingstone Castles, Sissinghurst garden, (if I only visited one castle it would be Bodiam), Rye, Lewes and Brighton plus many smaller places inbetween. You may be interested in a short-term National Trust overseas membership.

Are you not visiting London? Or Paris?

You can buy trains 5 minutes before you travel - on most routes, it will cost much more than buying 11 weeks in advance (can be by a factor of 10). I really wouldn't leave buying Eurostar tickets any longer than need be as these can be very expensive on the day of travel. There aren't many services a day to Calais and this isn't the most exciting French town to spend any time. You could get the Eurostar train from Ebbsfleet in Kent rather than heading to central London.

Are you getting the train straight from Calais to Budapest? This route goes via Brussels, so it would make more sense to take the Eurostar here rather than Calais. Flying would be a better option.

You could plot out an itinerary now for the England portion of your train trips. Once you have a date to travel, say from Liverpool to London, go online and buy tickets. Do this for each leg of your trip while in England. You'll save a lot by booking early.