re: "The client wants to send me details re job through my personal email. I assume this is OK bc how else do I and client send work back and forth?"
Upwork has no rules restricting which form of communication you use to communicate with clients or prospective clients.
You may indeed use email.
You could also use Upwork Messenger tool, Skype, phone, chat, texting, meeting in person... whatever works for you.
re: "I want to make sure client is legit bf giving my email. Client is ready it serms to hire me."
Well, there's no button labelled "Tell Me If This Client is Legit."
And there's no list to check.
If you are an experienced Upwork freelancer, you know which clients are legitimate and which are not based on their behavior and their job posts. We can identify scammers/fraudsters within a second.
If you are not an experienced freelancer, then you'll learn. The only true way to know if a client is legitimate is the client hires you officially through Upwork and pays you.
Yes, it makes sense to NOT SHARE YOUR PERSONAL EMAIL with a stranger. You need to develop your own rules and practices.
Many freelancers DO NOT SHARE THEIR EMAIL ADDRESS UNTIL AFTER they have been hired.
It is EASY to share information with a prospective client using the Upwork Messenger tool.
Another strategy: Many freelancers will create a "throw-away" email address for use with a new client. That way if the client starts abusing the privilege of having your email address, you can just delete the email address.
re: "Also, are they supposed to pay me directly through Upwork to make sure everything is legit."
If you and the client exchange money in any way outside of Upwork, then you are both in violation of serious Upwork ToS rules. Getting paid some other way is grounds for expulsion from the system.