This is the thing I am worst at, but I gather that it depends quite a bit on the product you are using and how it's applied. You may want to say exactly the product you are using, so that anyone who has used it can chime in. There are a lot of differences even between polys

I use a water based poly from General Finishes called "High Performance." You can apply it with a synthetic bristle brush, a foam brush, an applicator pad or a roller. I use a 2" Wooster sash brush or a 2" foam brush, and usually both. The mfg recommends no more than 3 coats. I use 6-10. I find that both bristle and foam brushes leave brushstrokes, and for me 3 coats risks sanding through. With 6 or more I can usually sand out streaks and other imperfections to get the finish pretty flat. There are at least two downsides with this finish. It takes a good 3-4 weeks to cure. It also takes a lot of careful sanding to get it flat. On the upside it has very little odor and very low VOCs. Also water based polys have the lowest propensity to yellow.

I think you can get quicker curing times and flatter finishes with solvent/oil based polys, but others here have more experience with these than I do.