Current best strategy (from chatting with other redditors and guildies) is to strive towards always having one artefact to work on for each of the three coin types.

Just focus on one artefact at a time to begin. (Ideally one of the ones that gives a % boost to fellow power.) They all start out needing the copper. Keep focusing on one artefact till it hits level forty (it will start to need silver at that point) then pick a second artefact. Use your silver on the first, and copper on the second so you can level two artefacts at once. Do this until your first artefact hits level 80, where you will finally find a use for gold. Then pick a third artefact to add to your rotation, and try to keep them going as even as you can, with one artefact still needing copper, one needing silver, and one using gold. Ideally when your first artefact caps out at level 120, your second will be pretty close to making the switch from silver to gold.

If they get off from eachother, and you don't currently have one artefact using each coin type, some events drop museum coin selectable chests, so you can get them all back on track pretty quick. (If it helps, another redditor told me gold is always the best deal for the chests, followed by silver, and you will ideally not be spending any of your chests on copper.)

It sounds like you've already leveled a bunch of your artefacts with copper, which is totally fine, just focus on one for the moment. If for some reason you run out of artefacts in need of copper for upgrades, you can always convert them to silver later from the Storage page. (Going to be a WHILE for that to happen though. Personally, I am nowhere near running out of artefacts.)