There have already been a few older sets containing pre-made mine carts or similar constructions with tracks besides the currently used style mentioned by IvanSanchez, take a look at how they were implemented:
Indiana Jones and The Temple of Doom (7199):
The Dynamic Duo Funhouse Escape (6857):
Amusement Park Roller Coaster (41130):
Silver Mine Shootout (...
I think you want to consider using the 4-stud-wide "rollercoaster" tracks, part numbers 25059, 25061 and 26022.
Here's how those to parts look like in set 60228:
The straight track are 8 or 16 studs long, and the 90° curved track has a radius of 12 studs (counted from the track centerline). These dimensions allow for a few track pieces to be ...