OK, so you’ve opened Nazjatar, but not started the Cloak yet.
You should quickly get your gear to 420-ish, pick up The Cloak, blitz it to Rank 5. After that, you will slowly but passively get gear up to 450 in World Quests. This is the same level you would get from Normal raids. This is enough gear in theory to start Heroic raids, but PuGs will expect more from people they are bringing.
430 is kind of the starting level for this patch. You will also want to chase the best Essences for your class and spec:
Here is a general guide to gearing up:
After the 420-430 level, your progress will mostly be through Mythic-plus dungeons. You do low-level M+, learn the routes and the approaches, work your way up.
You might want to consider looking at what’s good for the other specs as well, so that you have those as options for when you want them.
Here is a list of Alliance guilds on your realm with raiding progress:
Here is your realm forum, where guilds can advertise:
There’s a really nice group of people in the Alliance Community (cross-realm group) Scared of Dungeons
Now, when it comes to searching for a guild, in general, any level of guild might work for you. Mythic guilds often have lower-level raid teams as well. And organised guilds can pretty quicjly push you through M+ dungeons to get gear if they want you in their raid, so in guild context, item level is less important than knowing how to play well.
Should you transfer realms? … look around for a guild where you are, but if you really are motivated to make progress, you should probably get an idea of what the scene is like on busier realms like Silvermoon - or even also faction change and see the action on a busy Horde realm like Draenor. Horde is definitely more active than Alliance.