There are many different approaches, and almost all of them are right. Of course you now get used to do things a certain way. 25 years from now, if you see a novice doing things completely different from how you remember doing it, you may be tempted to offer advice like that, too.
If a something you hear troubles you, find a way to verify with an experienced third party. That's exactly what you did by asking on this message board, but for a question like this I suggest to look for places where you can ask experienced people in person.
Depending on where you live, your insurance may already cover a couple visits of a midwife during the first weeks, or there's a free midwife service provided by your town where parents can pass by every second Wednesday, or a hospital/church has a volunteer-staffed weekly advice afternoon, etc. Depending on where you live, there should also be a doctors visit when she's 1-4 weeks old, so that may be coming up soon. Just write these questions down and ask the experts. In the meantime you can be a bit more gentle just to be on the safe side.
To burp my daughter I merely held her upright at my chest, sometimes she burped, sometimes she didn't, and it didn't actually matter.