I am so sorry to say, but you are very unlikely to succeed in finding such a group.
I cry a little inside every time I read a post like yours, a new player who just found the game and is enthusiastic. I met a really nice old man, age 70, through a post like this one. I made a character, logged in, and played with him for a while, but I don’t play that much myself, and it was away from my own realm. I did find him a genuinely friendly guild on that realm. When I checked back a couple of weeks later, he was gone, and nobody remembered him. 
I still feel very bad everytime I remember that.
The game makes it very hard for the kind of friendly groups you are looking for to form, and especially to stay active.
Stage 1, I suppose, is levelling. Even new players who devote a couple of hours a day will get to 60 in a couple of weeks, and therefore nearly everybody is already at 60. It’s possible that someone will have an alt who is still levelling, that could play with you, but the odds are small that they would want to,
Once you get to 60, your chances improve A LOT. This is where the vast majority of playing time is spent, and everyone is the same level, so doing the same things.
However, you now need to find a guild or community of people who like to do the same things you like, play at about the level you play, and play at the same times you do. This doesn’t just happen; you need to seek them out. And since you don’t yet know what things you will like, it is impossible to target such groups in advance.
However, you should still be looking around now to get an idea of the types of groups available, and how they operate.
If you are trying to be competitive in the game, in the top 1% or less of players, clearing Mythic Raids and high level dungeons and arenas, the game does everything possible to accommodate you, but at lower levels of play, it will be all up to you.
Start by clicking around here: https://www.wowprogress.com/ and look for guilds on your realm, and compare them with guilds on other realm. Doomhammer currently has the “New Players” label, which means it’s a realm Blizzard are trying to get more players onto. You might also look at realms that already have high populations, and - and this is VERY IMPORTANT - on which your faction, Alliance or Horde, has an OVERWHELMING MAJORITY.
You might also look at this thread, though it is not very actime
I remember how precious those first few levels are, but if you stay you will be staying for years, so do take into account that the vast majority of your time will be spent at 60, and the more people of your faction that are on your realm then, the better your experience and chances of grouping with like-minded people will be.