Premium WordPress hosts will take away most of the pain from the responsibility of hosting Disciple.Tools. These hosts are usually marked by full-service customer support, fast servers with good response time, and pro-active security and server health monitoring.
WPEngine is a world class WordPress hosting service with great customer support. Their service is fast, easy to manage, and has free SSL security for your Disciple.Tools site. $25 / mo (last we checked)
Budget WordPress hosts (usually under $10 a month) have a pattern of weaker customer support, slower servers and server maintenance. You can still have great experiences with these hosts. All of these are recommended by WordPress.org on its public page.
WordPress.com is a great host for free simple websites, but they heavily control the themes and plugins allowed on their servers. For this reason, Disciple.Tools and the plugins developed for it are not compatible with this kind of shared, highly restricted hosting.