Flying into LHR, arrival 10 AM, weekday. Plan to take train to Middlesbrough out of Kings Cross. I looked at the BMI flight to Teeside, but it doesn't go until 16:00 and is more expensive. It will be two traveling, one UK, one US citizen, both carry-on. Cost is a factor. My questions are:

1. Planning to take tube to Kings Cross - seems easier than first taking HEX and then going to tube. Would be cheaper too. Any suggestions?

2. Want to buy cheapest tickets available for travel, looks like 48 GBP single for most times. When can I reasonably expect to catch a train out of Kings Cross and what happens if we miss the train I've prebooked - full fare? Should I buy for a later one and try to get onto an earlier one if I get there sooner?

3. The choices to Middlesbrough are GNER/Northern Rail connecting at Darlington and GNER/Transpennine Express connecting at York. What would be the most scenic, comfortable and/or convenient? Both take about 3 and 1/2 hours.

Thanks in advance for your assistance.