[sassan]

James:
You are a very good family person and I wish you all the best. In saying that, I hope you do realize the sensitivity of the issue, specially if your are going to be the official photographer of your sister's wedding. There are too many unknown variables here that I really can not give you any good advise frankly but let me break it down to some few simple lines that hope to get you somewhere.
You have received some good advise here from others but please pay attention to what Arthur53 and Postcardcv said.
In general for a wedding (Assuming it is going to be in low light / indoor / later day or evening time), you need to deal with low exposure, moving subjects and noise. A professional photographer typically uses a sensor that can handle these factors well and gives you the least noisy, sharp, well frozen image for the situation. This is best addressed with one of the newer full frame sensor cameras, whether DSLR or mirroless, but in an expert hand, a faithful camera, with attached right glass, can provide that good result, no matter which or what type. After all, the larger pie of a good picture is not about the camera but the person behind the camera.
None of your proposed options are full frame but then please remember the FF cameras are more difficult to use, specially if you are not familiar with it (Mostly don't have the on camera flash and their dedicated flashes are a totally different story to use properly).
I don't want to disappoint you from getting into photography shoe, specially the well rewarding field of wedding photography but have you heard that No surgeon operates on his own family members, even when she or he are the best in the field!
Please pay attention to historical data and experiences. You simply don't want to be the black sheep of family for the rest of your life, because something didn't work, despite your best wills and heartiest intensions.
If I were you, I would use that money you saved for camera or rental equipment as a down payment to hire a professional photographer for my sister (A very nice gift indeed that will be remembered for a long time, if not for ever. You can look around to find even a good photography school student photographer - comfortable with doing a wedding shooting-, for very cheap, instead of a well established expensive photographer.
But if there is an official photographer in the wedding and you are going to only take some family snap shoots, then go for it and best of luck. Don't forget the role of lens and flash/Light, in addition to the camera body.