Cost: Cheaper, because you're doing the work yourself and only paying for a VPS or two.
Time: A weekend.
If you're running a start-up and you can't hire a sysadmin, yes, managed hosting is a good idea and will net you a reliable system for a decent price. But if you're spinning up test/hobby projects which aren't mission-critical, take the time to build your own stack/servers. It takes a minimal amount of time and energy and will give you valuable experience you can use for the rest of your career.
Despite potentially talking myself out of work, I highly recommend this approach.
Sysadmin is something that you can learn by doing, and any competent software developer should be able to pick up enough knowledge to manage the kind of simple deployment that a freshly minted startup needs.
Cost: Cheaper, because you're doing the work yourself and only paying for a VPS or two.
Time: A weekend.
If you're running a start-up and you can't hire a sysadmin, yes, managed hosting is a good idea and will net you a reliable system for a decent price. But if you're spinning up test/hobby projects which aren't mission-critical, take the time to build your own stack/servers. It takes a minimal amount of time and energy and will give you valuable experience you can use for the rest of your career.