While I generally encourage people to consider primes over zooms, you're definitely in the territory here where zooms start to become more plausible. Before getting into that, a recommendation:

Your best bet is probably a DX zoom in the 10-24 range. You'll lose a stop of speed compared to the 14mm prime (most are f/4), but they will be much cheaper (~50%) and a little wider. I've never tried it personally, but the Tokina 11-16mm has a good reputation.

On to the comparison. Primes, like you say, are typically cheaper, faster, and of higher quality. But when it comes to ultra-wides, the situation changes a little, as ultra-wide primes have never been at the level of simplicity and well-corrected design that's been possible in the 35mm+ range, and zooms are rapidly improving. Sticking to Nikon only, here's the interesting comparison:

 Zooms:
   Nikkor 14-24mm f/2.8    $1800
   Nikkor 12-24mm f/4 DX   $950

 Primes:
   Nikkor 24mm f/2.8       $425
   Nikkor 20mm f/2.8       $600
   Nikkor 14mm f/2.8       $1700

 Fast Primes:
   Nikkor 24mm f/1.4       $2100

So even considering only the 14mm area, the fancy, fast zoom is the same speed as the 14mm prime, and only barely more expensive (one downside: much larger). Throw in even one other prime in the range it covers, and it's cheaper in absolute terms. The DX zoom is half the price, only one stop slower. Quality is harder to show in a chart, but Nikon says the 14-24 is as sharp as the primes in that range; pretty bold, but going on the review/testimonials I've read, they seem to be living up to that particular claim rather well.