It also depends on who you’re talking with. I wouldn’t go politer than ください for someone you’re speaking to in a normal, non-work setting that you would ultimately like to be friends with. Being too polite can kind of ostracize yourself.
This is probably a bit of a tangent, but my self-rule is that even if I’m speaking normally, I always use て form to make requests. None of that てくれ crap, especially when talking to girls. Sure if you’re a dude, you wanna sound like a dude, but people are much friendlier if you are still speaking somewhat politely versus straight up dude-talk. It also helps to add weight for when you really need to use strong, imperative speaking.
Anyway, from what I’ve noticed, お願いします is often said during the whole someone offers to do something and you have to do the reject it to be polite dance. “Oh, no, you don’t have to do that for me.” “But I want to.” “Are you sure?” “Yes, let me help you.” “Ok then. お願いします”
It can also help to reaffirm your request, but can make you sound desperate.
“Please help me this weekend!” （てください！）
“I’m probably busy this weekend.”
That’s just what I’ve observed though.