Have you looked into ram pumps (
https://www.youtube.com/watch?v=EV1yhnVCeJY)? Those are pretty slick, and you can build one yourself or buy one.
-or-
I have a Whale UF1815, which will suck up to 10 feet and push up to ~90 feet. The higher it pushes, the lower the volume. It has more flow than you're looking for, but it's rated flow is straight out of the pump, so by the time you get the height and friction in it might be closer to 2gpm. It has a filter built into it.
On the intake side, if you put a big pvc pipe (~3", maybe 2 feet long) in on the end of a flexible hose, you can drill a gazillion holes into it and then wrap it in window screen, and submerge the whole mess in the water. If you put it at a ~45 degree angle, most of the heavier sediment will accumulate at the bottom of the pipe, and you'll do a little per-filtering before it hits the filter on the pump.
I have mine just hooked up to a 150 watt
solar panel. When the sun comes out, the water flows. At dark, it shuts off. Pretty bland / easy.