A Mini or Nano could be a fairly good compromise between a custom designed PCB and an Uno. This might be the best place to start since the OP mentioned a lack of electronics experience, but a williness to learn (that's always appreciated on these forums 
).
Edit: Almost forgot about the other major components...
Here's an example of a compact four character, seven segement display module that uses serial communication. A tutorial and example code is available from the linked page. Directly controlling a seven segement display from the Arduino would be possible as well, but that would be easier to setup.
Also, here's an three axis accelerometer module.