Congratulations on becoming a home owner - how exciting!
Pretty much the main thing you need to look out for is water in the wrong place. This is what damages and destroys houses - if you can keep water where it belongs pretty much any building will outlast you, particularly one with stone walls and a tile roof. So pay regular attention to ensuring that the following are in good working condition -
Roof - try to find an angle of view that gives you a look at this every now and then, mainly for slipped tiles but also around weak points such as the flashing around a chimney. After a storm is a good time to look, and if you have access to an attic that will give evidence of any leaks. A decent tile roof will last for decades or even centuries, so highly unlikely to be a problem - keeping a casual eye out rather is the aim, rather than making it a constant worry.
Guttering - keep clear of vegetation/ice dams. This is one to check every autumn if there are trees nearby, or when snow starts to melt if you are somewhere very cold in winter.
Water pipes - know where all the stopcock/shut off/in line valves are. Any pipes in unheated spaces may need insulating against freezing (frozen water expands and splits water pipes, creating leaks when they unfreeze). If you are leaving the house for any time in winter shut the water off to limit the amount of water that leaks if you do have problems, and if you are leaving the house all winter in freezing conditions consider draining the system. The most likely problems are replacement washers in taps, a faulty toilet flush or a sticky ball valve in a water tank, all of which are potential DIY jobs.
Drains. As long as you don't put anything down the drains that you shouldn't (cooking grease, food scraps, hair, wet wipes, and so on) and don't have any big trees growing roots in the wrong places you can probably forget about your drains from year to year, but it is probably a good idea to work out in your own mind where the drains run and where the access points are, in case of difficulty. For minor blockages having a toilet plunger on hand is a good idea, and/or a drain snake.