My wife's road wheels are ~1200g clinchers. They're about 7 years old now (probably 7k miles). I had to replace one nipple a few years ago, but otherwise they've held up really well. They use Bikehubstore Ultralight front (66g) and Superlight rear (211g) hubs, Stans Alpha 340 rims (these were ~355g each), Sapim CX-Ray front and Laser rear spokes with aluminum nipples. Front wheel is 18h radial; rear is 2:1 24H with 2X drive side, radial non-drive side. With veloplugs, they weigh 1207g.
A modern fixed gear version would use a Raketa or Mack rear hub. Otherwise, I don't see much reason to change things. For the rear wheel, an old-stock hook bead 29er rim might save a few grams versus the current batch of Alpha 340 rims. For the front, you should stick with an aluminum rim for braking power. You could have a <1300g clincher wheelset for <$800. Depending on your weight and riding style, increasing the spoke counts to 20 front and/or 28 rear might be wise.