How do you save your passwords on your iPhone?

Hi all! I have an iMac and an iPhone. I keep all my passwords on my iMac using Keychain. Many times, I manually input information into keychain to remember what email, password or other information I used to sign up for various things... including web pages and apps. I just got off the phone with Apple tech support. I wanted to know if I could have keychain on my phone. I guess I already do... for safari. However, I want to access the keychain information I manually input. I guess there's not a way to do this (access that information in keychain on my iMac while on my iPhone).

So... what do you all use to keep track of passwords? Is there an app that will let me use it both on my iMac and on my iPhone? That's what I want. The Apple tech guy said to get 1Password (or OnePassword). Would that do what I want? I'm not familiar with it.

Thanks!

julie