Seconding everything Melooon said, including "don't both with salting" - a salt only exists to make it harder to reverse-engineer a password if you've got the hashed version: so long as the (one) password on this site isn't one that you use
anywhere else, that's probably not a concern for you anyway! (And by the time somebody's gotten onto your server to see the hash, you've got bigger problems than them being able to log in to your admin area!)
Just don't forget to check for $_SESSION['is_admin'] on every single page that needs it. I see lots of people do things like make a login page (which checks a password and sets a session), then create a page that handles
creating posts (which checks the session and then does things), and then create a page that handles
deleting posts (which just deletes things without checking that the
$_SESSION['is_admin'] is set and... uh-oh, that's a problem!).
Don't forget to add a logout link that goes to a page that unsets the session variable and then redirects back home, or whatever! You never know when you're going to need a logout link!
And finally - and for a small personal site you definitely don't need to think about this rightaway - down the line,
consider the possibility of cross-site request forgery attacks. E.g. if you have a page that (a) checks you're logged in as an admin and then (b) deletes a post... is it possible for an attacker to put a malicious link in an email or on their own website that, (if you're logged-in when you're tricked into clicking it) goes to that page, resulting in a post deletion? The risk is inf
initesimally small for a small personal site unless you've made a lot of enemies!
Love the direction you're going in, anyway.
PHP empowers the world of the "mildly dynamic website", a particularly magical and special category that's close to my heart.