What is the best laser (or machine/treatment) for 'permanent' hair removal?

You sound like the perfect candidate for hair removal! At my office the laser we use for hair removal is the Alexandrite from syneron candela. It works wonders! Lasers send targeted, controlled pulses of light through the skin that are absorbed by the melanin (pigment) present in hair follicles. This energy is converted to heat, which then destroys the hair follicle (without harming the surrounding tissue) and significantly slows down their ability to re-grow.
Since hair grows in cycles, the number of treatments varies by patient skin type, hair color, and hair coarseness. But it typically takes about 6 to 8 treatments, spaced every 4 to 8 weeks. Additionally, annual touch-ups may be required to keep you completely hair free.

At Monroe Comprehensive Laser Center in Monroe, Mi, we highly recommend the Gentlemax Pro from Candela.  It has both an alex and a yag laser platform and can be used safely and effectively on all skin types from 1 to 6.

I rarely attempt to remove hair on the face and neck because typically it is very fine. If this is the case, treatment might actually lead to more hair paradoxically. With light skin, the best laser to use is an alexandrite, 755 nm laser. I recently purchased the Splendor X laser and I believe it is not the best laser on the market. It actually uses 2 wavelengths to attack the hair simultaneously. BBL is not great for hair removal but the Lightsheer is. 

The result with your type of skin and hair .i.e.fair skin with dark hair should get good results with laser like lightsheer. I would advise you to consult a dermatologist to rule out any hormonal causes and if required, to put you on medical treatment along with laser therapy for optimal results.