Is there a list with the best gems to use on specific weapons/etc in the armory?

If not, looking for recommendations for the following items. Numbers are how many slots are in them.

3 3 4 1 1

Also is this a good set? Includes also Phoenix Quill and Soma Tablets. It seems to be great. Pet is Tier 8

I also have

Sorry, relatively new to actually getting and using a decent set with a good pet.

The modifiers act the same for all weapons and some weapons / modifications are better suited for certain challengers. Blessing of Natural Armor Tear Crystal is a pretty good catch all if your absolutely lost in the process. It has a blessing that when activated will block 2 of each icon type and protects against freezing.

From there you adapt the crystals for what your sets lacking - i.e. ones that add extra icons your opponent isn't blocking or ones that add defense your set is lacking. If your opponent cannot be frozen - you wouldn't want to use weapons or modifiers that freeze.

I wouldn't go out and buy a bunch of Modifiers at T8 - you can earn them from grinding challengers or the battle shop for free.

Is there a specific challenger that makes you feel like your set is inadequate? What is your overall budget?

Cursed Effigy, the Tormented I can never get...

Question, with the Blessing of Natural Armor Tear Crystal... do you only use 1 or more than 1 works? Does it work if you have 1 on each item being used?

I usually use two per item, but it depends on the opponent. You can only activate the blessing once, but by stacking the crystals, you increase the chance of the blessing to activate.