DeployHQ has always been flexible and easy to use with a variety of different servers, with support available for FTP, SSH/SFTP, and other proprietary services and protocols such as AWS S3, Shopify and Rackspace Cloud Files.
Within the SFTP and FTP space, DeployHQ can connect to almost any hosting provider on both dedicated server platforms, and shared hosting. With the general ease of setting up a server on a shared hosting platform (most will support SFTP for optimal security and upload speed), it's straightforward to get started.
To help with setting up connections to popular shared hosting providers, we've written a number of guides that can be found on our website, tailored to each provider:
https://www.deployhq.com/guides
And we're always looking to add further providers to the list - so if you have one you'd like us to write a guide for, do let us know.