in the beggining there is a lot of testing for, amm trite and trate, after a while you should almost never have to test ammonia or trite unless something appears to be going wrong. just trate. then the other important tests would be alkalinity, ph, cal, thats all I test weekly. if I have an algae problem I'll check my phosphates too. its good to have almost all the tests on hand just in case, but after a while you kinda get a feel of how things look and you'll cut back on most of your testing. I wouldnt w2aste money on strontium test kits or magnesium, mag you can calculate by subtracting your calcium hardness from your general hardness, and that will give you a close enough number for mag. as for other trace elements if your using a good enbough salt mix and have good water change rituals they are being replenished faster than all but the most insanly stocked tanks can use.
cal, alk, trate, ph IMO are the most important.
forgot specific gravity also.