Which realm to choose?

To answer your direct question, all I can advise is that you read solidly through

and follow the links to find promising guilds.

However, if I were you, I’d make a start on whatever it is you want to do beginning from where you are, with the character(s) you have.

Changing realm will not magically make you more eligible to play PvE or PvP, and you haven’t really started on either, even at the low end, so it’s not like you’re specifically looking for a Mythic progression guild or a 2400+ team. You can get into lower level PvE and PvP content just as easily from anywhere. I would find it demoralising to pay for a transfer or level a new character and then find myself making no progress in the new environment.

High-pop realms with your faction in an overwhelming majority are better for the obvious reasons, but I will say that AD Horde is an exception. AD is big enough that Horde, though a minority, are a decently sized minority, and still have plenty of people to be viable and form a community. And of all the realms I’ve seen, AD has the best sense of public community. CRZ destroyed all other realms, but the RP barrier saved AD.

Entry- and mid-level PvE and PvP can be done from any realm quite easily, and in your shoes I’d establish a track record and experience on AD, and only then, when you’re getting into the really competitive areas, consider whether you need to move.

Join these:

Community:

Discord:

These are cross-realm groups that do low to mid level M+ and raids, in a friendly atmosphere.

That covers your PvE.

I don’t know about PvP. I do know that the best way to start is to grind random battlegrounds. While I see you have done some, you could certainly do a lot more.

There are PvP Discords. You can find them easily enough with a search. I don’t know enough to recommend one.

I do know that realms matter little for PvP purposes, except rated BGs, because there is no need to keep teams together. For arenas, it’s up to you to make connections with people and play with them regularly.