Short answer is that you can use BBpress on wordpress and that can be migrated to Discourse…
That’s what I sensed. Honestly, I would say pick PHP based or Discourse now and stick to it, rather than doing php and then trying to migrate after. You’re just going to confuse whatever members you have by doing that. Not to mention the time you’ll spend on the migration and re-coaching your community members. Plus, I’d argue your adoption rate is going to be higher with Discourse honestly.
On cost, the biggest challenge you are going to have is building an engaged community. Accounting for the time and effort it takes to build a community, $5-10/month is a pennies.
If community is core to what you are doing and you are on a tight budget, perhaps consider downgrading the package your WP install is on to free up funds for Discourse.
My 2c, set yourself up now and just go all-in on Discourse. Otherwise a facebook group might be a good idea. I’m taking some liberties here not knowing your full situation.