Do the solo instance and garden of knowledge to get yellow basic PvE gear, then proceed to Narakali and holy tower for purples and makarna/prometuns for Red PvE gear. Use server wide lfg at the dungeon entrance.
As for pvp gear, buy basic yellow stuff from the genesis crystal vendors, upgrade it at the blessings npc accordingly. Getting one shot is a thing you've gotta get used to for a very long time due to the extreme p2w factor.

Long story short, do the same quests and instances every week

Pretty much what accuracy said. I also suggest joining some legion. You could easier go to instances with your legion members. If you are more pve, than pvp player spend genesis crystals and get steadfast pve gear. You can get pretty decent stats from 1 week's worth of garden/mirash/steadfast gear.

Asking for advice is always a good thing, but don't forget to discover things and taking your own path at the same time.
What Accuracy and zerhunter68 said are good guidelines for starting out in Aion.

What I suggest to new players who want advice:

1. Level from 1 to 75 at your own pace.
   
2. Level from 75 to 80 and make sure you do the dark blue quests and early campaigns to get a full set of Lakrum PvE & PvP gear.
   
3. At level 80 you can do 4x Mirash per week [You can enter earlier but I advice getting 80 first unless it's on a tuesday and you're close to 80 (Due to reset)]. Mirash is a solo instance so you won't need to find group members. Mirash will give some Ancient items that are better than Lakrum.
   
4. If you are a chanter or cleric you can try solo'ing Garden of Knowledge(GoK) as well. (Ask on LFG for someone to hold the group open or create a second account for group holding purposes). If you're any other class it might be better to find a group through LFG or server-wide recruitment. Duo'ing GoK is possible even with lakrum gear. Repeat this each week because GoK gear is sufficient to do Narakkali and Holy Tower.
   
5. After reaching level 80, you should also do the Lakrum Garrisons each week. Depending on your server/faction these might be hard to do alone due to competition & enemies (the higher number garrisons also have stronger NPC's so take that into consideration). There should be regular groups looking for these or if you can play at late hours you should be fine alone untill you meet other people also doing garrisons.
   
6. When you reach a garrison for the first time you will get 10 free ancient PvP enchantment stones from the NPC. Don't use these on Lakrum gear. After you've done a full trip of garrisons (there are 9) you will have 540 crystals with which you can buy a PvP weapon (I advise 'Brave') and then either PvP wings (I advice 'courageous') or the steadfast PvE weapon if you use a 2-handed weapon (Greatsword, polearm, staff, orb, book, bow, aether key, stringed instrument). If you've gotten the weapon from Garden of Knowledge then you will fuse that one with the PvP weapon (making sure the PvP weapon is on top) and won't need to buy the steadfast. If you have enough crystals, buy the PvP boots as well.
   
7. Wether you get a Garden of Knowledge or steadfast weapon first, reroll the stats untill you have attack/cast speed before fusing under the PvP weapon.
   
8. With the 90 free ancient PvP enchantment stones, you should make all the PvP items to +11 (Weapon, boots, wings) and afterwards go for +15'ing the ones you can. If you're lucky they might all end up with +15.
   
9. Every week repeat doing Garden of Knowledge, Mirash's Refuge and the Lakrum garrisons. You'll notice a big curve of damage after you replace the Lakrum gear, and soon you'll be able to solo Garden of Knowledge which means more money for you.
   
10. Once you have like half a set of Garden of Knowledge you should try finding groups for Holy Tower and Narakkali. These aren't hard instances and will drop Legendary gear. You can find groups with server-wide recruitment for these if you don't see anything on LFG.
    

Important - Try to do the following as often as you can depending on the time you can spend ingame.

• Ashutanel Dredgion (3 times) each day
  
• Runatorium (1 time) each day
  
• Sieges on tuesday, thursday, saturday (lakrum sieges) and sunday (divine siege)
  

These will give you a lot AP, some enchantment stones and legendary/ultimate idium which is required to upgrade your gear. Even if you lose! You can go to sieges alone and you can enter A.dred/RT with the quick entry feature in case you don't find a group.

Misc

• Try to join a legion to play with others and get to know people.
  
• Do luna daily & luna weekly each day/week as you can get enchantment stones there and luna materials to craft enchantment stones.
  
• You can reroll stats on gears (with kinah), I suggest to reroll ancient PvE gear to physical/magical attack + (magical) accuracy when it's possible and crit + (magical) accuracy when there is no attack. (Magical) Accuracy is very important because you will miss hits (= low damage) on the bosses without. Also try to get attack/casting speed on your weapon and run speed on your boots.
  

And don't be afraid to ask questions on the board!