[...] The fastest travel speed is approximately 60 ft/min, which translates to a minimum of 100 Hz sampling rate (for the .125" accuracy) and the longest run will be 2,500 ft.
100Hz leaves you plenty of time!
Even a very cheap microcontroller is able to do 1MIPS, so in the 10ms you have per sample, there's room for at least 10'000 instructions.
My question is what micro controller/programming environment is going to he hefty enough to handle task but user friendly enough for novice programmers to develop this tool in a years time.
You really dont need hefty, but rather user friendly, easy to learn and with a large user base, making it easy to get help and code snippets.
I'd recommend an Arduino for its huge support by other users and if you feel a need for more horsepower, one of the 80MHz PIC based chipKIT's
which are code- and interface compatible with Arduinos (Like an Arduino on steroids).
I was looking at this board for the gyro as it already has a kalman filter built in and seems to be rather user friendly.
This board alone could do what you want, by interfacing the encoder to it, but I have my doubt about its beginner friendliness. It might be worth a try though, if you're going to buy it anyway.
Alternatively, you could get the "raw" sensors - and probably save a bunch.
Would we be able to pair this with an encoder?
Do you have a particular encoder in mind or...?
Getting an encoder with SPI or IIC interface would be a good idea if you want to interface it to the board directly.