Hey there! Welcome to wow! First things first, there are a few ways to search for a guild for yourself.
On the forums:
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Try posting in your realm forum, here: https://us.forums.blizzard.com/en/wow/c/frostmourne/67
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Searching through the “New player friendly guilds” thread, here: (Make sure to look for guilds listed as based on your realm, Frostmourne) New Player Friendly Guilds Check In Here!
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Take a look through the guild recruitment forum, here: https://us.forums.blizzard.com/en/wow/c/recruitment/oceanic-guild-recruitment/45 Keep in mind most guilds advertising as recruiting will be looking for raiders, but there are social guilds that post from time to time as well.
For all of these options, make sure the guilds you’re looking at are Alliance, not Horde.
In Game:
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Check out the guild finder tool. The “J” Key by default will bring up your Guilds and Communities menu. The guild finder tool will be in it’s own tab in this menu.
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Approach guilds that advertise in a city’s trade chat as social, casual or new player friendly guilds.
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Tell trade chat you’re new and looking for a casual/social guild to show you the ropes.
Keep in mind that finding the right guild for you is not always an easy process, so don’t be afraid to leave a guild in search of another if it isn’t providing you with the experience you’re looking for.
Now on to your questions. 
Do I keep leveling up on Eastern Kingdom ?
You can level in Eastern Kingdoms until you hit lvl 60, at which point you’ll receive an automatic quest popup giving you the option to go level in either Burning Crusade or Wrath of the Lich King zones.
Currently, the leveling structure is as follows (Though this will be undergoing a complete revamp in Shadowlands, so if you’re somebody looking at this in the future, this could be outdated.)
1-60: Eastern Kingdoms and Kalimdor
60-80: Outland and Northrend
80-90: Pandaria and the zones that Cataclysm added to Eastern Kingdoms and Kalimdor
90-100: Draenor
100-110: Broken Isles
110-120: Kul Tiras and Zandalar
You should get pop up quests each time you’re able to head to a new zone. If you reach one of those level thresholds and don’t receive a popup quest, return to Stormwind and it should pop up there.
Note that you will not experience anywhere close to all of the leveling zones on your first play through. So don’t be afraid to skip some and try them on the next character you level.
When should I leave Eastern Kingdom ?
Also answered above.
What else’s can I do other then quest for leveling ?
Completing dungeons in the Dungeon Finder tool (i key by default), Battlegrounds (H key by default, fair warning, battlegrounds are PvP content.), Pet battles, and collecting Ore and Herbs (Mining and Herbalism professions required) will all grant you experience.
im really unsure i download the retail or classic.
Rest assured, you’re playing retail lol. It would take you a couple weeks to get from 1-40 in Classic 
Also, your forum avatar would say “Wow Classic” by your name if your character was from Classic.
If you have any other questions, feel free to reply, or make a new topic in the “New Player Help and Guides” subforum, here: https://us.forums.blizzard.com/en/wow/c/guides/new-player-help-guides/33
Over there we have a few regulars including myself that are always happy to get new players pointed in the right direction, and between us all can get you an answer to pretty much anything.