I guess this project will be battery powered, so none of the above.
Maybe Pro Mini, and the 3.3V version of it. Use 3.3V components where possible to fit with that. On the other hand, I hear a lot of complaints on the forum that running an SD card adapter soaks up almost all the ram memory that Pro Mini's atmega328 has, so maybe something compatible with Arduino Zero, i.e. based on a samd21 chip? Something based on that chip would have a much faster CPU clock speed and SPI clock speed, so better able to deal with the speed calculations and SD card writing. Plus it has extra hardware UART to interface with the GPS module.
I'm no expert on GPS modules, so I'll leave others to recommend something.