Why did polyurethane make wood feel coarse?
First of all, I'm assuming you already sanded the surface smooth enough before you started. If you put polyurethane on a rough surface you will get a rough finish.

Second, as @keshlam says, make sure there is no dust at all on the surface before you apply the finish. A slightly damp cloth can help pick up anything remaining (but make sure the wood is dry before you apply). Also, don't bother trying to apply a finish in a dusty environment, that's just asking for frustration.

Another possibility is that you kept brushing over the finish as it dried, which is a common beginner mistake. Moving quickly, do a thin coat over the surface and then don't go back to touch it up. Small bubbles may form on the surface as air comes out but it will be OK. If you keep re-brushing over the finish as it gets tacky you will leave the surface rough.

Finally, your chosen brand (Minwax) is perfectly fine, so no particular concerns there. If the can has been sitting a while make sure you stir it before using, but don't shake. You don't want to introduce unnecessary air into the poly.