As a member of our club told me when I went on one of my first big runs with the club, "minis can go anywhere". Based on some of the locations I have been with them, I would have to agree! Take care of basic maintenance, carry a few essential spares - basically anything you can think of that would stop you dead, and that you can change at the side of the road .Carry a few tools that would allow you to do those jobs and also carry some spare fluids. Having done all that, I would go anywhere in a mini without any more (and maybe a bit less) concern than I would have in a modern car.
There is just so much less to go wrong in a mini, and they are actually really reliable in my personal experience of them. I think also because you are more involved with them through regular maintenance, and just paying more attention to any new sounds / smells etc, you tend to pick up on any issues that may be developing which gives you the chance to sort them before they become something that could leave you at the side of the road.
If it hasn't been done already, maybe changing over from points to electronic ignition would be a worthwhile move, and probably adding the ignition weathershield that was fitted to later cars would be a good idea. I have owned SPi's for years now which have them, and I have never had the old classic issue of rain water shorting out the electrics, despite driving in all weathers. They really do a good job of keeping the distributor and wiring dry.
But most of all enjoy your mini. I think you will have a great time with it, might be an adventure at times but it will be the making of lots of good memories.