Pretty much common and uncommon will be food for your rare+ champions. There are a couple of exceptions - as there are a few uncommon champions that are great at specific things but general rule of thumb - focus your energies in to your rare and better champions.

The best bet is to experiment with various artifacts.  Pay attention to which ones have what stats attached to them and what you feel will most benefit that particular champion.

For example, for your "attack" champions, things like increased attack, crit, and other offensive stats are going to be useful.  On the other hand, when it comes to HP or support champions, it might be more feasible to go with HP or defense stats.

So, in one case, a 1-star epic might be better, but in another case with another champion, a 3-star common might be better.  

Since leveling up at the lower levels is not particularly expensive, level up various artifacts and compare their scaling for yourself to see what you feel is most viable for your champions.  And it's not just about the stats on the artifacts, but the set and how viable it is for a particular champion as well.  

Hello

A 3 star uncommon will always be better then a 1-star epic, not sure if I have ever seen these but here's why.

The primary stats of an artifact increase per star level(rank) so for example, a 1-star chest piece will give you a lower % of stats than a 3-star chest piece, this difference is quite substantial.

The thing is with a 1-star epic piece, though the sub-stats may be good those extra stats will be quite low, so you would be trading off a decent proportion of primary stats for a small %  benefit to some stats but does this outweigh those primary stats, in most cases no.

it's worth noting that weapon, helm, and shield will always be flat stats(not a percentage), so these are all about the substats.

Gloves, chest, and Boots can be flat stats and percentages, I would strongly suggest that you use % based primary stats on these pieces, the exception to that advice is accuracy, resist or spd stats where these will always be flat stats. for example, speed primary is only available on boots, so if speed is what you're after, this is suggested.

I hope that helps.

many thanks

Hello

A 3 star uncommon will always be better then a 1-star epic, not sure if I have ever seen these but here's why.

The primary stats of an artifact increase per star level(rank) so for example, a 1-star chest piece will give you a lower % of stats than a 3-star chest piece, this difference is quite substantial.

The thing is with a 1-star epic piece, though the sub-stats may be good those extra stats will be quite low, so you would be trading off a decent proportion of primary stats for a small %  benefit to some stats but does this outweigh those primary stats, in most cases no.

it's worth noting that weapon, helm, and shield will always be flat stats(not a percentage), so these are all about the substats.

Gloves, chest, and Boots can be flat stats and percentages, I would strongly suggest that you use % based primary stats on these pieces, the exception to that advice is accuracy, resist or spd stats where these will always be flat stats. for example, speed primary is only available on boots, so if speed is what you're after, this is suggested.

I hope that helps.

many thanks