Also, generally speaking, the works that appear in non-paying venues are of lesser quality than those of paying. Which is why if you have a bunch of random token or non-paying credits on your cover letter it's a big red-flag to pro publishers. It's worse than no publications at all, because it tells them you probably aren't up to their writing standards, whereas no publications could simply mean you're new. And they know that new doesn't equal bad.
So, don't shoot yourself in the foot. How will you know if your work is pro-quality if you don't submit top-down? If you start with the lowest possible market, how are you to know when you're ready to move up? Subbing to non-paying markets, but wanting to be a successful writer, is kind of like saying you want to marry a nice guy someday, so you're going to start by dating jerks. It makes no sense.