Hey @jhanna,
First off, welcome to the 1 Series family and congrats on your 125i!
If your aftermarket wheels are the correct size, you should be fine. Run flat tyres don't require anything different and don't have any extra sensors that would be incompatible with aftermarket wheels.
Beyond that, here are a couple of thoughts. You may know all this already. If so, please accept my apologies.
1. A good tyre shop can answer any questions you have about wheels and tyres and how changing things will affect your car positively or negatively. Also, the Tire Rack learning center is a great place for basic information:
https://www.tirerack.com/tires/tiret...ch.jsp?tab=All
2. If you want to use the same tyres (or the same size tyres) on your new aftermarket wheels, you should probably get wheels that are the same width as the stock BMW wheels (we can help you find the stock wheel specs if you need them). If you can't find the wheels you want in the stock widths, you can look up your tyre specs on a site like Tire Rack or the tyre manufacturer's website to find out what width wheels your tyres will fit. See the 'rim width range' column in the picture below (this is for the original width tyres for the 1 Series M; it will be different for you car's narrower tyres).
3. When it comes time to replace your tyres, you might want to look into non-run flat tyres. They usually provide a better ride than run flats and you'll enjoy your BMW even more.
4. When it comes time to get your new wheels, there are several measurements you'll need to take into consideration. The bolt pattern and centerbore should be the same as your stock wheels. Wheel width, diameter, and offset can vary depending on what you're trying to do, but in general, staying the same or close to stock will have the least possibility of having fitment problems or adversely affecting your car's handling.
Hopefully, this helps some. Ask away if you have more questions. You posted this in the 1 Series M subforum. You might get more responses on the main 1Addicts forum, but we can help you here, too.