Most RP of the casual kind can be found without joining a guild. Basically, there are what’s called “RP hubs” such as Stormwind or Duskwood, where a lot of casual or “walk-up” RP happens. Then there are public events every now and then such as the masquerade ball in Dalaran not long ago. I’d recommend checking out Argent Archives www. argentarchives .org to look for upcoming events like that.
As for Guild-based RP that is more to the casual side rather than epic stories with heroes and villains, there are some like (what I have seen) the Redbrew Company or Copper Crown that run taverns, or Dustcloud Corporation and Traders’ Initiative that run stores (Copper Crown also runs a store from what I’ve seen). If you play a vulpera (or maybe just any horde race) there seem to be a lot of “caravan” guilds around. Might be interesting for you as you said you prefer a traveler-type character.
The guild I’m in (“we’re contractors, the good kind” - Zithis) often has combat-related events ending in some kind of boss fight, and sometimes a recurring villain, but also has a weekly in-character meeting for our characters which is more on the casual side. So it’s possible to find a little bit of both in a guild, though I can’t really speak for other guilds.
Also I would recommend getting the addon Total RP 3 if you haven’t already. It really helps, trust me. It allows you to make a “profile” for your character that others can see in game, but even if you don’t write anything in your profile, it’ll help, as you can see other people’s profiles and others can see you’re a roleplayer at a glance just by hovering their mouse over your character.
Oh, and welcome!