Arduino

http://www.instructables.com/id/Make-your-own-Arduino-on-Veroboard/

Try using an lcd with SPI, they're cheap on eBay.

Pro-Mini Setup

• Pro Mini : $4.62
• 5110 : $1.97
• 3v3 step up: $2.07
• Battery Clip: $0.50

Total: $9.16

This gives basic functionality, MCU, power and display. Buttons are cheap, so are most sensors.