I get the train to London Bridge about 8/half past and tend to get a seat, especially if I'm later rather than earlier. Back of the train as other have said.
Overground: probably no seat. I never do but then I only get it when the trains are screwed so it's always going to be bad. Then it's no room for people at Brockley onwards and I find it gets pretty stuffy. If you have to do the Jubilee change, get off from the front, and go UP into the ticket hall and back down again to avoid the hideous scramble that is the down escalator.
Having taken the Tube to work in the past, I find the train much nicer.

This is all from FH, HOP I think you'll be lucky to get a seat. Might on the train if you are towards the back.
And as other have pointed out there are going to be LB works which will be hellish. It's already pretty grotty and they've not started properly yet.