Although I'm not familiar with Discourse self-hosted, I would wager that it's just like any other forum, in terms of resource needs. VPS will work better, but for small projects shared may suffice.
The requirements are Ruby, Redis, PostgreSQL, so a lot of generic shared cPanel hosts probably will not work.
I do see that A2 Hosting
currently offers it, and they're an excellent hosting company.
Many more people run it on VMs, everything from a cheap DigitalOcean droplet, to better VPS plans from hosts like Namecheap
, and others.
Budget matters. What's the budget.
But be realistic.