Whether 'tis nobler to suffer the slings and arrows of trying to photograph a black cat in a coal-hole by purchasing a lens that looks like it should be on the front of a spy satellite or to take arms and buy a flash kit and actually see what it is that the camera is pointed at...
Hamlet, omlette, or roulette aside, I vote for the flash. I am just not sure which I prefer - mains powered kit or portable speed lights. I've tried both and they both have their advantages and disadvantages.
To clear one thing up at the start - if you are starting out afresh without the comfort of 40 years of gear acquisition filling your closet...or hanging round your neck like a plastic and aluminium millstone...the cost is going to be remarkably the same. An entry-level strobist kit is very close to the price of an entry-level studio kit. The chief difference between the two is the power supply and whether you'll want modelling lights.
The strobist kit comprises two lightweight light stands, two umbrellas and appropriate holders, and a carry bag. You'll need to add two speed lights and a wireless radio command kit to this, plus two sets of one-use lithium AA batteries.
The entry-level Elinchrom set contains two stands, two strobe heads, two soft boxes, and an in-built radio command set. You'll want to add a long extension cord and powerboard from Bunnings
In both cases we're talking about $ 1000 new stock.
The strobist kit is neat to transport - one case - but you'll still need to bunk the flashes in your camera bag. The Elinchrom comes in two cases that hold everything - plus you need to carry your camera case.
Advantages of the strobist? No need for an AC mains outlet nearby - no power cord on the floor. Disadvantages? No modelling light - limited light modifiers. Many batteries to remember. Markedly slower to recharge between shots.
Advantages of the Elinchrom? More light, faster recharge, unlimited number of shots. Neater integration of package - more light modifiers available. Modelling lights. Disadvantages? Gotta have an AC mains power point available. Two power cords on the floor.
For me - with all the stuff I need sitting on the shelves in the studio or at home - it revolves around the AC mains outlet and the distance I'll have to haul the gear from the car to the shooting venue. Short distance and power available means the studio strobes go out for a job - no powerpoint or a long walk to the venue means the speed lights.
Heading photo - Princess Fee at the Pseudoskirt rehearsal. The skirt of power! And the socks of polishing the floor!