Tiers range from Tier 1 (must have) to Tier 5 (Almost useless or useless).
There are 40 artifacts in total, each time you obtain you'll need more relics to obtain another. Relic cost will depend on artifact capacity.
Must Have All of these artifacts will help you in all aspects -- damage, gold, relic increment, and stage reduction.
Should Have These are artifacts that give you damage, gold, and relic increment. However, their bonuses aren't as needed as tier 1 due to one of the artifact bonuses is not that useful enough to be in tier 1.
Ok to have If you have nothing else to salvage, you should keep them. Their bonuses aren't bad but not great either.
Salvage if not needed These artifacts has one useful bonus but the other bonus downgrade them to be in tier 4.
Almost useless or useless These artifacts have bonuses that are not that useful enough. Other artifacts have better use for W2.