How big is your tank? what is your bio load? do you have live rock? how much?
By trace minerals your LFS worker probably means what I refer to as trace elements.
Trace elements are elements in the salt water which out reefs consume. Example's would be calcium, magnesium, iodine, etc. These elements can also be added, I dose calcium and alkalinity, as well as adding Aquavitro fuel twice a week. I also change 10% of my water weekly and only use RO water for top ups (tap water can contain unwanted minerals). You need to be testing and adjusting your water levels accordingly if you wish to keep a reef.
Some people do run skimmer-less tanks, not me though. If you do wish to run a skimmer-less system then i would be recommending 25% weekly water changes.
A skimmer job is to remove organic waste from the water, which if left in the tank would turn into nitrites, ammonia, nitrates, phosphates, and all sorts of nasties that will harm your fish, corals and inverts.