Thought I'd post some Beijing specific thoughts after living here for 1.5 years and my own experience. Hopefully it helps with your trip.

If someone asks you at the airport for a taxi ride probably don't want to except this (unless you don't care about money). Same goes if they want to take your bags for you. Minimum, they'll want a tip. This is actually a good rule for pretty much anywhere in the world.

After you pass customs and get your bags the taxi stands are two levels down. Follow the signs. This area is usually not that busy and sort of looks abandoned but you are at the correct place. Go wait in the queue. At this point I've had non-official taxi drivers still approach me. You want to walk to an actual waiting taxi when it's your turn in line. Even the official people working there won't stop you from walking off with a random person.

Unless you speak Chinese have a printed copy of your hotel/destination in Chinese (or a saved picture on your phone). There is pretty much a 0% chance your taxi driver will be able to read or speak English (or your particular language). You need Chinese money (i.e, yuan/kwai/RMB/CNY -> all the same thing) to pay for the ride. They aren't going to to take credit card. Or if you have WeChat Pay or AliPay you can use that but if you have those things this post is useless for you.

Alternatively, you can order a DiDi to the airport if you're signed up but make sure you go to correct pickup location you set on the app. I've had success going up a level from the baggage exit area. I'll post another thread about DiDi.

There is the Airport Express train as well. It's supposed to be cheap and easy to get into the city where you can then take the subway or a cab/DiDi to your hotel. I've never actually taken it so look it up if you want to go that route.