Hi (name)

This is how most business e-mails in English start out: with a simple greeting ("Hi", "Good morning", "Hello") and the recipient's first name:

Hi Lana,
Can you send me the proposal we discussed yesterday?

Thanks,
Liz

Depending on your culture, this might seem too casual for business e-mail, but this is the most appropriate style for writing to someone within your own company. It even works for writing to people outside of your company if you know them or if your e-mail is just about something simple.

Hope you're well.

This is a phrase that you can use to start a casual email. It means "I hope that you are doing well."

You can use this greeting in emails to friends, coworkers, clients, etc. If you'd like to make it more formal, include the subject "I" at the beginning:

I hope you're well.

You can also write "you are" instead of "you're" for more formality:

I hope you are well.