Sounds like a cool project!
What would I need Pinoccio wise to setup 5 buttons/lights around my basement.
Depending on how bright/big you need the lights to be, I think a small neopixel strip or ring would probably be perfect, and they're both small enough that you can run them straight off of the Scout's battery. If you don't need the control and color variation that neopixels give you, you could just get a couple super bright LEDs.
As for the button - again it depends on your needs. Any button will work, so you could go small or big.
For Pinoccio gear, you'll need at least 5 Scouts (for your 5 buttons). If you throw a WiFi backpack on one of them, that'll get the whole Troop hooked up to the internet.
An awesome alternative to the WiFi backpack, and something that we've only just now released (docs coming soon), is Bridge Mode. This lets you plug in (USB) any 'ol Scout to a computer, and use that as the Lead Scout for the Troop. Instead of buying a WiFi backpack ($80) for one of your 5 Scouts, you could just buy a 6th Scout ($60) and keep it plugged in to your computer while people are playing the game. Bridge Mode is actually faster and more stable than a WiFi backpack for stuff like this.
What would I need to get the times and scores back to a database on a server?
Nothing. Pinoccio does all of that automatically. The buttons will trigger pin change events automatically, which will be broadcast and recorded by our server (or yours if you want to run your own). They'll be timestamped and available via the stats API.
You would use the API to set up the scoring and what not. Everything that happens to the Scouts is automatically and immediately streamed out through the API.
Good luck! Please post photos/videos in the Projects category when you get it going!