Best way to present multiple signup options?

I am building a web application where users sign-up using their real name, phone number or email address, and a password. I'm building the form and right now, after a user enters their name , they have the option of entering either a phone # or an email. BOTH input boxes are displayed on the form (with labels), email first, with the word 'OR' in-between (and a message that reads "both is fine, neither is not"), then phone. Example form:

<form method="Post" action="signmeup.php" >
<input name="first_name" type ="text">
<input name="last_name" type ="text">
<input name="optional_email" type ="text">
OR
<input name="optional_phone" type ="num">
<input name="password" type ="password">
<input name="password_verify" type ="password">
<input name="submit-button" type ="submit" value="Create Account">
</form>

Should I just have one input field visible in the form (like just phone) and give a clickable link that will switch the input type to email if the user would rather sign-up using their email (like Facebook does)? My idea is that if users sign-up using both a phone # and email, upon logging them in (their data has been verified and entered into the db) we give them the option of picking which contact method they'd like to use as their primary contact method with us. The other would then be used as a recovery account, like if the user forgot their primary account #/address. What are your thoughts on my current approach, and what improvements would you make?

EDIT 7:17 EST

I see this same sort-of question has been asked before here, and I'm leaning towards adding a radio button option where users can choose to either input their email or phone number. This seems to be the most straight-forward, easy-to-understand approach.

link to where I found this solution, posted by user DA01: Combining email and phone inputs into a single text field