It's a bog ordinary Wordpress multisite installation. The most exotic thing about it was WP-supercache and WPEngine have clever inbuilt logic to safely disable that when you migrate across.
I'm more curious what VPS package you had powering your stuff at Linode and how much you were spending on it each month? Reason being that 250 USD buys a LOT of server these days and it is surprising you ended up with underpowered hardware if your VPS wasn't giving you any problems.
If you're looking to upgrade in the future, you might be much better off throwing a dedicated server at the problem and setting a nightly backup to S3. Also, thank you for posting.
If you're looking to upgrade in the future, you might be much better off throwing a dedicated server at the problem and setting a nightly backup to S3. Also, thank you for posting.