I can tell you how it worked when we started our studio, it may or may not help you:
Before we decided to open professionally we did what I would call a "soft opening." (We didn't call it that at the time). We own our own commercial building which is our studio space (a luxury, I know), so that was luckily a non-issue. We decided on a fictitious name, registered our tax ID and name with the state and were "above board" from day one.
We were working with our personal "prosumer" gear at the time. We consciously decided to hold off on pro gear until we were certain that we would make our money back on our investment.
We bought some simple paper backdrop rolls (your standard black, white, grey) and a nice brown mottled canvas back drop. We bought 2 tungsten soft boxes (entry level stuff; easy to correct for the color in LR). We already had LR, PS, and a good computer from our lives as "hobbyists."
When we needed to move the light source in the studio we unplugged them and rolled them over. We also shot on location in town and in the country (which we still do).
After about 3 months of operating like this, we were swamped with business. Referrals were rolling in and we were booking up to 6 months in advance.
We took a trip to
B&H. We ran up a 10K bill buying a D800, top of the line zooms, and strobes. It was a fun time. If you can, go buy your gear in person. It's a great experience, and seeing and touching things before you buy helps you avoid pitfalls.
Within 3 months the 10K bill was paid off. For the rest of the first year we put most of our earnings right back into our craft. We spent a boatload. Now, we only buy things when they break or when we really think we need something that our current gear can't do.
This was 4 years ago. We currently book up every single season (focusing on weddings, senior pics, and a ridiculously successful Christmas holiday season (books up a year in advance!). We book families on a limited basis as we only have room certain times of the year. Whew. We ended up being successful!
Now, your idea scares the crap outta me! I think you should rethink your plan. Be a bit more conservative out of the gate. You can buy more as you go, but if you buy it all upfront, you could be out 20K.
Please let us know what you decide. Best of luck in your endeavor, just think it through!