Actually, almost all of the privileges that are available to mods are available to non-mods, provided that you've received enough rep to access those privileges. The only exception (I think, I'd have to double check) is access to PII such as a user's IP address, email address, etc. Mods sign some paperwork stating how that stuff can and can't be used.
I'll second Criggie's suggestion that you pick a badge and work toward it. I hadn't thought of that, but I like it.
Ted's point about varied skills resonates too. You could play to your strengths, looking for places where you personally have a skillset that is especially applicable.
Another approach is to focus on the most recent privilege that you've been granted as you gain more reputation. For example, your highest privilege (1000 reputation) at the time of this writing is that you can see vote counts. Pay attention to vote counts. Get a feel for what the community votes up, what they vote down, and what posts get both up and down votes. When you hit 2000 reputation, you'll be able to edit posts. Focus on improving posts through edits. Once you hit 3000 reputation, start paying attention to when you think something should be closed or reopened. And so on.
In the end, anything you do to improve the site will be appreciated. And since everything you do is subject to consensus through votes and/or peer review, you won't do much harm if you make a mistake or two along the way.