Where is your final destination in London? This will determine whether King's Cross/St Pancras or Liverpool Street are viable options, as well as whether you might want to take a Thameslink train and stay on past St Pancras.
Looking at
Realtimetrains on a random weekday in the future, it appears that the 0709 train attaches a portion at Cambridge, which is scheduled to come in empty at 0648, so you should have a good chance at a seat if you arrive early enough. Can someone with local knowledge reveal whether the empty portion is usually unlocked before the other portion arrives (allowing people to board early and wait in comfort) or whether it is kept locked until the other portion has attached (requiring people to queue up outside in the cold)?
The 0653 starts at Cambridge, arriving at 0638 in service from King's Cross. I believe you can board as soon as it arrives, and it supposedly has plenty of seats available. (Similarly for the other Thameslink trains every 30 minutes.)
Do you want to have a proper table, a fold-down seatback (airline-style) table, or are you happy with just the seat and no table at all? On a class 387 (e.g. the fast Great Northern trains like the 0709), I believe almost every seat has some sort of table, while your best bet to get a proper table is the cluster of 4 tables (16 seats) under the pantograph in the middle of the train, but the drawback is you have to put up with a few loud bangs during the journey. On a class 700 (e.g. the Thameslink trains like the 0653), the only proper tables are in the first-class sections, 22 seats at the very front of the train for which you need a first-class ticket, and 22 at the very back of the train where you only need a standard-class ticket due to that section being permanently declassified (so you might need to turn up early to bag one of those), while I believe in standard class some trains have seatback tables and some have no tables at all.