nmg85

If you did want to get the standard thameslink train you need the area labelled platforms A/B they go frequently and I think the fare to London bridge is about £3.50 / can use oyster / contactless as well.

Maybe look into the Sky Garden - Its a viewing platform with amazing views that is free, you just need to book tickets in advance which are usually released 3 weeks in advance.

Green Park is a bit of a trek to cross between lines in my opinion. I would get a thameslink train to London Bridge and then 2 stops on Jubilee to Waterloo. Where is your train coming from into St Pancras? To be honest most trains at that time heading into London will be very busy.