For options under US$1000:
nOrh se9 - Integrated amp. Sounds good w/stock tubes, but sounds much better when some good NOS tubes are rolled in. This can get expensive and offset the low entry price of the amp.
ASL OTL32 - Nice, versatile, low-cost headphone amp. Works as a decent preamp too. Needs some tube rolling to sound best. Not the most powerful, but does have an XLR connection specifically for the K1000. Works great with other headphones too.
Dared 300B monoblocks - These have volume controls on them, so a preamp is not absolutely necessary. I generally love the sound of a 300b tube, but the same comments as the nOrh regarding rolling. I like these a lot.
RKV MkII - Headphone amp only. Sounds great stock, no tube rolling required & replacements are cheap. You do need a 1/4" adapter for the K1000's.
Classic Fisher tube amps/receivers - those I've heard had great synergy with the K1000 (I don't remember the modesl #'s though). May be difficult to find in good condition, or may require expensive refurbing. As always, rolling tubes can get pricey.
SAC K1000 amp - I've never heard this amp, but I've always been curious.