I have had some deeply uncomfortable experiences with Uber/Lyft drivers and sexual harassment. Some not even subtle or possible to misconstrue. I had a trick set up where if a driver was making creepy comments, I would text my sister I was making a safety call to her and place a fake phone call to her and pretend she was my boyfriend and say things like "Should be there in 15 minutes honey, on "x" street, see you really soon." Just to communicate to the driver that (1) am in a relationship/not interested in the driver; (2) someone would know right away if I went missing and (3) I wouldn't be alone at the destination. So if you have a friend who might be willing to do this, it can be helpful.
The worst experiences were pretty much always when I was ubering in the middle of the night or very early morning (I had a job where I frequently got home after 2am and also had to sometimes catch very early morning flights for work)--so I recognize that I have some "weirder" uber/lyft experiences than what is typical. To that end though, I'd recommend trying to book flights when you know you'll be taking off and landing at regular times (to the extent possible--always a possibility of delays).
One safety tip you should ALWAYS follow is confirming the license plate number matches the one the app so you don't get in the wrong car. This is for safety and also to make sure you don't accidentally get in someone else's uber/lyft and wind up at the wrong destination!
I also recommend keeping your app open and watching the route so you'll know if the driver is taking you the wrong way, and then you can correct them. I have heard accounts of sexual assaults by uber/lyft drivers where the victim said after they wished they had spoken up when they could see they were going the wrong way.
I know this all seems overkill to a lot of people, and is obviously not the norm. But it does happen, and these are simple precautions that aren't a real inconvenience so I definitely recommend them.