You need to find out how high the water needs to travel. It doesn't really matter how far, just how high.
Eheim 1260 and 2260 Water Pump
For example, this pump says max pumping height is 12 feet. That should be enough to go up one story. Listed price is $134.
If you build the sink higher then normal the pump won't have to push the water as far which could put you into a cheaper pump. I didn't look at any other brands, but now you know what to look for it should be easy to find what you need.
P.S. Powerheads don't pump water, they just move water around to create flow.