I have a 2 speed pump and a mechanical timer. The speed is manually set at the pump. Simple.

You need to make sure your new pump's output at full speed doesn't exceed you cart filter's capacity, or it will damage your cartridges--to much pressure will tear the paper.

Don't be confused by the "Bigger Horsepower" thing. I suspect (and this is a W.A.G.) that with your pool, a full-rated 1.5 hp is the BIGGEST pump you should use, and only if it's 2 speed. You may be fine with a really high-quality full-rated 1 hp. If so, that's what you should get.

But I'll let the pump experts give you more detailed advice. In the meantime please list the model and size of your filter. They'll probably ask you how it's all plumbed as well.