I don't think your only choices are between an unmanaged VM and a managed Drupal stack. In my experience simple shared hosting is all you really need. Unless your project/website is eating up enough resources or other security needs require a VPS or dedicated server. But since you're considering managed Drupal stack I'm guessing that neither of those are a concern. And as long as what you're trying to do doesn't require apache modules that the shared hosting provider doesn't allow or provide. But as far as the basic Drupal configuration is concerned you really only need rewrite, php, and either mysql or postgres. Which are all provided by any shared hosting provider.
I currently run my site on a shared hosting account at bluehost. They also provide some automated scripts through the cpanel which can use to install Drupal but you don't have to use those. Since they give you shell access you can install Drupal yourself and use Drush to manage it. This is the route I've gone. I have complete control over everything related to Drupal as far as theming and modules go. While Bluehost maintains the server, apache, mysql, etc. I only have to make sure that I keep Drupal installation up to date.