Which one is Takashi’s older brother?
The delivery guy today had exactly the type of face I go for.
I can’t help thinking about my older brother’s nose hair.
This word starts with an お to make it more polite. Then it has the kanji 兄 which you already know. Lastly, it has さん which is an honorific to elevate people and be polite. This is basically the formal way of saying older brother (versus plain old 兄). It can also be used to refer to a guy that you don't know who has a youthful appearance.
The reading for this one is pretty tricky, and I'd consider it an exception. To remember it, you have to learn the 兄 part, and everything else will fall into place. Here's a mnemonic to help you:
Your (kind) older brother pushes you down on the ground. You stand up and look at your knee (にい), which is all bloody. "Why'd you do that to my knee!?" you ask. "You're supposed to be a nice older brother, that's why I call you お兄さん!"