Buggs, the first thing I would tell you is to use the filter and get rid of any boots that aren't speed. After that, sell all gauntets and chestplates that aren't % based (i.e. flat ATK=20 ATK vs ATK %=5%). Hold off on the RES and ACC as you might need a few later on. the last thing would be to sell all of your remaining artifacts that don't have SPD as a substat. This will take longer since you can't tell what doesn't have a substat, only what does. Once that is done and you've got enough silver, start upgrading your artifacts straight to level 8. If you haven't gotten at least one additional roll on SPD, sell that artifact.
Keep in mind that you should probably be focusing on properly gearing out a single champ at a time, based on their prospective role in the team. Don't spread your best artifacts too thin. 1 great champ is, generally speaking, better than 3 good ones. You'll get more good artifacts.
Example: Let's say you just got PainKeeper (I use her because I just pulled her). She is HP based, all of her abilities are on her Allies, so you don't need any ACC in your build. You'll want Boots with SPD Primary STAT, preferably with HP% substat; HP% gauntlets, SPD/DEF%/RES Substats (You don't want her getting stunned/frozen), HP% Chestplate (Same substats as Gauntlets). ATK does nothing for her as she is HP, so for the top row you should be looking at substats.
Keep in mind this changes if you have a tank or a nuker. Crit rate/Crit DMG become much more imprtant then. I'm still not good at creating a nuker. I can't seem to get the Crit Rate/Crit DMG high enough for a good nuker.
As for the Life sets, I would say that you keep the good artifacts and don't focus on sets, for the most part. If you can get 5 and 6* from the forge and get good Resilience, and are getting 5 and 6* Divine Life artifacts, then yeah, sell the life. Remember Sets are a bonus, not a requirement.
There's a TON of better information than I can provide in other threads on this forum from the MODS (Who all know what they are talking about) and other people who have been playing for a long time and all provide great advice. Some times it can get confusing since they respond in Telerian, while you are speaking your native tongue.