Before going down this process you should know how much a developer sign-up worth to you. You can always buy growth, but you need to know if you can buy growth profitably. Generally look to get a short term value plus a life-time value calculate ROMI. It wont be accurate but do the best you can.
Between Google and FB, I've found Google search is the regular winner but the ROI gap is narrowing these days. There's some good hacks you can use to access your audience cheaply if you get creative. I would recommend you trial display as if done well this could provide better results than search (where most companies go first).
There's a pertinent quote for new products: "A great ad campaign will make a bad product fail faster."
Make sure your monitoring not just sign-ups, but how long people stick around etc.
Best of luck.