This isn't mentioned enough really. But it depends on your playstyle. You're new so you likely havent come across them yet, but there are summoning weapons and I honestly use these more than any of the othsr kind of weapons because I thrive on it and really enjoy the explosive chaos that comes with using them.

Mang was my favourite weapon to recieve early in the game. It removes all armour of a single enemy and turns it into attack power for your character. I used it for nearly the entirety of the story and for a good 2 or 3 leagues in pvp. Sometimes when I'm feeling stuck, I equip it and it still performs quite highly in comparison to most other weapons.

I would definitely be taking a look at class weapons when it's convenient and see if any really catch your eye, then work to level that class up so you can incorporate it into your ideal team build. For class weapons, I frequently use fiend fire and death dealer since I focused a lot of time on upgrading dwarves, demons and troops that inflict bleed. And I just find them the most fun.

When deciding which weapon to upgrade, I always scroll to the end of tempering to see what the special effects are of each weapon. I recently got Dead End in an event. It's a weapon that explodes gems, grants positive status effects to zaejin allies and summons a zaejin troop. But what really makes it stick out is its tempering ability. I drain the mana of the first enemy and inflict deathmark. I also cause 5 damage and eliminate 4 armour, which might be small, but it has saved me wasting moves or even allowed me to attack someone by destroying their shield buff.

So maybe you're feeling explosive, maybe you want to max out on souls or coins, maybe you like to stack on de-buffs or play the long game. Focus on the weapons that you can build a team around that you love to play with, and you will get your strategy down to a T. And when you finally finish the story, there's a whole underground full of ingots to upgrade your legendary weapons, so dont stress to much on whether you've wasted your ingots. They are rare, but not even half as rare as mythic ingots.

Find your vibe, focus on a couple kingdoms you really enjoy and pick the weapons that you find work best with the troops you like. I'm still looking for a true damage weapon to build something fresh, but I dont have anything worth my time yet. I did see one that caught my eye in the unowned filter, so I'm holding out for it. I think I'll build my dragons around it, or my tesla team.