(Incidentally, I guess this app would deliver a vast load of numbers. Is there a program that could interpret them, or would I need a maths degree to do it myself?).
Looks like it will give you a spreadsheet with columns for latitude, longitude, time, speed, altitude etc. So it should be fairly simple to convert that to GPX. eg try GPS Babel, it can convert from various CSV formats.
My main questions are about demands on the battery and the requirements of the SIM to be acquired (ie how much data use?).
This depends on just how often you want to log your position. ie one point per second or once every few minutes, or every hour etc.
Would also depend on what phone you are using, and what apps are running, and how good the phone signal is etc. Best to test it yourself. Would probably last a few hours of logging at one point per second.
In terms of data, probably a kilobyte or so per point. Not sure if using Google Sheets would have any overhead of extra data, compared to uploading in plain text.
For an app, I like GPS Logger for Android:
http://code.mendhak.com/gpslogger/It is designed to be lightweight, and battery efficient. It has loads of options for how frequently to log etc, and can upload in various formats.