Good afternoon, I would like some guidance on how to progress to obtain better equipment and weapons. I have already finished G1 of the Book of Blaanid. Should I continue with G2 or start with dungeons? My main talent is Warrior and I use Dual Wield. Thank you and I appreciate the guidance since I haven't played Mabi for about 10 years.
#Progress in equipment and weapons for better performance
turbid holly
compact phoenix
Welcome back to Mabinogi! My advice is to continue with Generation Quests for now, and accumulate more levels and skill ranks!
-# I'm assuming you're Human and dual wielding One-handed Swords here - if that's not the case and you're a Giant dual wielding one-handed Blunt Weapons, please pretend that's what I'm saying. 
Blaanid's Weapons and armour will carry you forward quite a way. Around G13, you'll unlock something called Chronicle Missions where you can acquire another pretty decent One-Handed Sword to paired with your Sword of Blossoming Memories called a Celtic Royal Knight Sword. (https://wiki.mabinogiworld.com/view/Celtic_Royal_Knight_Sword) As that weapon gains proficiency and upgrades, you'll be good up until around about G22 - where you'll unlock Tech Duinn Missions and may be able to create a pair of Perseus Steeled Swords (https://wiki.mabinogiworld.com/view/Perseus_Steeled_Sword)
As for Armour; Blaanid's Memorial Flower Outfit will honestly be more than enough for the entirety of the story. Armour investments are trivial early on, but later on when you clear G22, look into the Geas Devastation Set! (https://wiki.mabinogiworld.com/view/Cethlenn_Set) Or even better, shop on the Auction House for second-hand pre-reforged gear. Set Effects and Reforges are the go-to for power in Armour, but that's something to get into a bit later.
When you reach Cumulative Level 20k (which Blaanid will help you with), you'll gain access to Arcana Talents. If you're still a dual wielding warrior by that point, the Elemental Knight Arcana would probably suit you! So while you're training skills, work on getting the Grandmaster Talents for both Warrior and Mage, too!
Hope that helps. 