My pump (standard home type sump pump from Home Depot) sits in a big rubbermaid tub under my sink. I have two holes cut in the lid. The sink drains into one hole. The pvc you see here, from the sink, stops open ended just inside the lid. The pump drains out the other hole, through a check valve (the black rubber piece), and up where it turns to fall towards the sewer connection. It's hard piped with pvc all the way. I don't use a p trap. There is always water sitting on top of the check valve, so sewer gas isn't an issue.
The float on the pump (and pretty much any pump) can be adjusted to allow the water to fill to a level with which you are comfortable. Mine fills to about 4 inches from the top before the pump kicks on.