Overseeding and lawn renovation...

Hi guys,

Newbie here both to the forum and to gardening.
I have recently moved house and for the first time i have a lawn. (5mx20m). The lawn looks ok from the kitchen window (fairly even colour and no major bare spots) but upon close inspection is full of moss and thatch. So, after a bit of research and consultation I have come up with this plan of action.

Cut (done)
Feed (done)
Scarify (doing today, hired an electric flymo scarifiyer)
Prick the lawn with a fork
And finally overseed
Wait a good while, mow high and gradually reduce height.

My question is this. Iâ??m not very sure how to overseed. There is a good bit of conflicting information out there and im scared of putting down too much seed (causing disease) or too little (causing a bare lawn). I believe the best way to do it would be to make a seed â?? topsoil/sharp sand mix and spread that but not being an accomplished gardener Im not sure how to do this and dobbies from what I can see only sell Seed, not a pre-ready mix for overseeding.

Can anyone advise me on the best way to overseed my lawn after I have scarified it.

I have included a picture of the lawn in question.

Thanks very much for any help.