I love induction furnaces but don't get me wrong here, you may not need induction as badly as you will need capacity. I have attached a screenshot from a crucible size for a 3 kw induction furnace on amazon.I am buying a very small (3kw) induction furnance, (~150$), I don't have many experiences with induction furnance.
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The small U shape on the left is the inner crucible which determines the capacity to melt. This thing is tiny, and is probably rated to hold 1 kg of 24 karat gold. Maybe more, I didn't do the math, but it is way too small for your needs if you want to eventually process 3 to 6 kg of alloy a week.
I remember back in the day when I learned about density. The trick question they asked was "What weighs more, a pound of feathers or a pound of lead?" The answer is they both weigh the same but the real point of the question is to show you the difference in density and what a big difference it makes. Well, that feather lead analogy applies to melting metals as well. Silver is roughly half the density of Gold. So that tiny crucible will only hold half a kilo of Silver.
Let me preface this answer by saying I am old and have done this stuff for many years. I refined large quantities for many years before induction became available so I know for a fact that what you want to do will work perfectly well with a gas furnace. Realize gas furnaces take longer to heat up and are louder when running. If you have customers bringing in melts you may appreciate a faster quieter melt. But even then, whole jewelry pieces take up space and that crucible for a 3 kw furnace doesn't have much to start with. You should be thinking about melt capacity and you will see gas melting will get you the capacity you will need for a lot less money. If you decide to inquart with Silver to refine you will need the capacity. I would suggest a gas furnace that takes a #10 crucible. That will handle inquartations and all of your melt needs. Another benefit of gas furnaces is you can put a smaller crucible in the furnace to do smaller melts. That isn't doable with induction.