You can pick which artifact set you get, but the stats are still RNG – you can’t pick the main stat or substats. The 4 artifact sets available are:
Gladiator’s Finale Wanderer’s Troupe Noblesse Oblige Bloodstained Chivalry
The Artifact Strongbox’s worth depends on how you spend in the game. Generally, the Strongbox is only worth using for the Gladiator’s Finale and Wanderer’s Troupe artifacts. This is because they’re the only artifacts that you can’t get from artifact domains. Aside from the Strongbox, you can only get them from Trounce domains and boss drops. Each Trounce domain is limited to one run per week. Plus, farming 40-resin cost bosses just for 1-2 artifact drops is never worth it. Because of this, using the Artifact Strongbox is far more resin-efficient. As for Noblesse Oblige and Bloodstained Chivalry artifacts, it depends. These two sets share the same domain. So: If you need artifact pieces from both sets, it’s better to farm that domain – using the Artifact Strongbox isn’t worth it. Any extra artifacts you get are better spent on leveling good pieces. But if you only want one of the sets, using the Artifact Strongbox can be more resin-efficient. You can continue farming another artifact domain and just use the extra artifacts for the Strongbox. And, unlike domain farming, the Strongbox guarantees the artifact set you want. Its only disadvantage is that you’ll get the artifacts at a much slower rate. The Strongbox only gives one 5-star artifact for every three 5-star artifacts you offer.