First is the plate loads. Leave some room to convert to cascode circuit. You'll need one more gate-stopper and MOSFET. The heat-sink will get put on the new one, so a bit of flexibility in the layout will probably be useful. One sounds good. Cascode is bloody fantastic. Build with one first, and keep in mind there is some pedal left when you feel the need.

Any rectifier with less than 2A of heater current can be used. 6AX5 and 6BY5, and smaller the 6X5 are octal options. I just got my new PS choke in the mail from Heyboer, a 30Hy monster, at about 3x the current capacity of the small hammond and a quarter of the DCR for the new linestage design... At ~$80 it is a fair fraction of the entire cost of this project, so perhaps later. HTS 8039 if you feel the need.

If the 5687 has too much gain, 12B4 is a good sub. Two of them are required, and heater load is comparable to a 5687. You'll need a third 9-pin socket...or keep the 5687 and get an output TX. So many cool options...
regards,
Douglas