Submitting to literary journals is quite the adventure! Though it has been many years since undergrad, I still have a curated list of journals provided by the professor of a creative writing workshop. A handful of those journals have since become defunct. A lot of them are niche or ultra-competitive--not exactly great bets for an "emerging" writer.
Poets & Writers' classified pages and literary journal catalog are other places I've found calls for submissions. Some of those posts inspired me to write a piece even if it didn't eventually find a place in the requesting publication. Themed submissions especially can be fun writing prompts--so, not the worst way to spend some keystrokes.
For a while, I coasted on Submittable. There are some awesome journals available there, and the running "Discovery" tab ordered by deadlines helps me decide where to submit first. Sometimes, though, a call for submissions sounded like a good match--up until I perused the journal itself online and found my piece wouldn't exactly match up.
Then I joined Twitter and was blown away by some of the journals I found there! I would have totally missed these journals if I hadn't joined Twitter. Some of them accept submissions via email only, so they have no presence on Submittable. Some of them are new, or not yet listed on Poets & Writers. However, they are publishing high quality writing, interacting with the community, nominating writers for recognitions, and publishing the work of emerging and established writers alike.
The kindest rejection letter I've received so far came from one of these smaller journals. They even recommended other journals to submit my work to, based on my aesthetic. That letter truly helped me feel like a legitimate writer and member of an artistic community.
So keep your eyes peeled for great opportunities, and just keep putting yourself out there! Research each magazine you're interested in, especially if you aren't already a subscriber or regular reader. You want to make sure your work is a match--and that they are a reputable editing team with a masthead and so forth.
We got this!