Just sharing a few of the ways I approach literary contests and magazine submissions (at least, when I'm not under my smut pen name). This is not a how-to-win guide, more of how to organize your ventures so you don't want to pull your hair out. It can be hard to know where to start, and I can't tell you what trail to take, but I can definitely hand you an outdated trail map from a hotel lobby.
1) Tracking and scheduling is important. It can take up to 10 or more submissions for a work to be picked up by a mag, and contests are an even trickier thing. I approach this like I do with book agent submissions: A giant fucking excel sheet, organized by genre, deadlines, review timelines, and my personal preference. This will save your butt for publications that don't accept simultaneous submissions, and will make sure you don't send a rejected piece back to the same people twice.
2) Consider avoiding high value contests, and focusing on lower payouts that have less competition when you first start out. There is a sweet spot between unpaid writing and $2000 prize pots that you have to find for yourself. Mine is anything above $25 a piece for accepted flash fiction, yours might be more or less, might be word count based, might be based in prestige and recognition rather than payment. Only you can decide what will feel satisfying as a sort of payment or literal payment for your work.
Look for smaller publications and magazines that specialize in your style, or ones that you can write pieces specifically for. If you see low cost contests or piece-wanted ads, try to find some who have pushed their deadlines back once or twice-- this often means they have not gotten much traction, and you have a smaller pool of competitors.
3) Choose the right piece. Or write the right piece. There are two primary methods of going about this. You can either find competitions and mag submissions, then go through your backlog to find a suitable piece (or write a new one if you don't have a perfect fit), OR you can take one very polished piece from your collection and try to find publications that will suit it. Either way, make sure that you are giving your stories their best shots. A horror publication may not be interested in horror erotica, even if they are similar. A lit magazine may not accept stories about animals, or sci-fi.
You need to get a wide cast, but make sure you have a hook on the end of the line.