About an English discussion:
Shall I start first? Shall I start first? (both you and your partner spoken at the sametime)
The Chairman: Shall we start the English discussion right now; are both of you ready ?
Oh ! I'm not ready yet. You had better start first..
Oh ! you better start first.
Oh ! it's lady first.
Oh ! I'll let you start first.
Pardon me ! If you don't mind I'll start first.
If you tend to let him/her first, you may say 'Maybe you start our discussion/ Maybe you take the lead.'.
If you tend to start by yourself, you may wait for one to two seconds and then say 'Maybe I could start our discussion./ Maybe I shall start first.'.