Ask the client what they want you to do & charge for, especially if it's pricy.
If in doubt, book second-class for what works out as the cheapest and fastest way to fulfill your duties. So if you're in a meeting at 8 am in Edinburgh & you start in Penzance, Easyjet; if it's Manchester at 11 and you leave from Fulham, train it. Show client, without boring them rigid, that you have come up with the cheapest but best way.
that is what DH does - he goes ALL over the country, sometimes clocking up over 1200 miles a week all days are worked out fee plus expenses - mileage plus night in hotel for any more than three hours away and then quoted as a block price per day / two days / three days depending on the event AND he charges more for London on a Friday because of the M3 coming home!
We gave London rates and rest of the country rates. We always include our expenses in our rate. The only exception is overseas travel. DH has threatened to double his rate for any future trips to the Isle of Man and Switzerland because they are so boring. If overseas travel is required we always travel flag carrier or at least not sleazyjet or ryanwhocares.