How would it be possible to allow the user to choose what content they want to see on my site's home page, which has at least 5 distinct sections which take up a lot of space. I would like the options chosen by the user to be stored in the database so that the user's options can be retrieved from the database the next time he/she logs in
You've already answered your own question. Store their preferences on the database. So next time they log in, you fetch their preferences from the database and include the content they want. For example:
if ($preference == "weather") {
include("weather.php");
} elseif ($preference == "sports") {
include("sports.php");
}
Don't use that code, it's ineffective, but it gives you an idea of what i mean.
Diego