When you go up to the Southeastern High Speed area it is in the far north east corner of the station, as far as possible from the Underground. There are stairs, a couple of escalators and a lift to get you up there so that part is pretty easy.
The High Speed Javelin trains have no First Class or reservations so you can sit anywhere on the train. Seats are padded but not a lot, and quite comfortable. The ride is very smooth and you will be up to speed and back down again for Stratford International station where the most recent London Olympics was held. Then back up to speed for crossing the estuary and onwards. They tend to run to time. Whilst there are toilets and luggage racks there aren't any other amenities. There is nominally free wifi but because a lot of the trip is in tunnels (in order to make the tracks straight so the speed can be high) wifi is at best spotty.
That said the journey is fast so you won't miss what's not there. Get your coffee from one of the many outlets you will pass between the Tube and the train as you walk the length of the station.