Derek,
The lighting needn't be complex. Christopher Beane, who was (is?) a pre-eminent flower photographer, did some with just the light from a doorway. IMHO, the key is to have diffuse light and direct light, the latter to add shadows and depth.
The big decision is choosing between continuous lighting and strobes. I use continuous lighting. I want to be able to see the approximate effects of changes in lighting as I move lights around. You can do that with continuous lighting or with strobes that have modeling lights. You can't do it with a regular flash.
The advantage of continuous lighting is that it is simple and cheap. I use two "hair lights", the small light booms that portrait photographers sometimes place above a subject's head. In the US, cheap ones run about $100 each. One of the two I have is
this one, or an earlier model of it. The important thing is that one should have a socket to hold an umbrella (that one doesn't; B&H's store brand did when I bought mine). I use halogen lights for now, although I plan to switch to high-quality LEDs once I solve the problem of finding compatible in-line floor dimmers. I usually use a 75W pointing up into a reflecting (silver) umbrella for the most diffuse lighting. I use a 50 W in one for direct lighting, and I cover that one with a diffuser. (Baking parchment paper works as well as anything fancy, but you may need two sheets. I then move both of them around until I have what I think I will like, take a test shot, and revise.
This simple arrangement is enough to give depth to the photo, e.g.,
The big disadvantage is the long shutter speeds this requires. If you are on a concrete floor or have the flower on something extremely heavy (like a stone countertop), this isn't so bad. If you are on a wooden floor, which I am now, it is a real pain, because the slightest movement can cause the flower to move. This matters more with some flowers than others. The worst has been the numerous milkweeds I have done, like this:
I use a remote release. I flip the mirror up (using mirror lock-up) and stand stock still until I am confident that nothing is moving, then trip the shutter.
I don't have a photo of my current setup, and it is not up now, but here is a photo I took when I was first using this sort of arrangement. The main difference is that I replaced the white umbrella with a reflective one.
I'd like to try studio strobes with modeling lights to avoid the slow-shutter-speed problems, but it would be a considerable investment in time and money. Perhaps someone here who uses them can chime in.
I hope this helps.
Dan