It sounds like you could use a minimal server setup to run your Moodle courses. One of the important aspects is how many concurrent users you expect. With 8 - 20 people taking courses at a time, the requirements are minimal ($5 per month for 512M memory, 1 core CPU, 20GB storage).
Re: "Some courses would have a live component" -- Moodle has several options for integration into online classroom services and platforms. One of the more popular platforms is the free and open source BigBlueButton (BBB). In case you haven't seen it already, you can try Moodle and BBB out for free as long as you like on: https://moodlecloud.com/en/ The UK's Open University uses Blackboard Collaborate for it's OU Live sessions.
Re: sysAdmin, a system administrator isn't a Moodle admin. They're two very different but equally important jobs. A sysAdmin looks after your server, typically Linux, Apache, MySQL, and PHP upon which Moodle is installed. If you need to modify or adjust any settings, e.g. change the frequency of the cron job, increase/decrease the server memory limits and script timeout restrictions, database settings, deals with malware and attacks/hacks, etc. this is what a sysAdmin does, as well as updating all the software including Moodle when new releases, bug fixes, and security vulnerability fixes are released.
If you want someone to do both jobs, I think it's easier for a sysAdmin to learn to be a Moodle admin than vice versa.
I hope this helps!