There are really two questions here:
1. What CAD system should I use now?
Fusion360 is awesome. Use it. If it's doing the job you need it to do, there's no reason to use anything else for your day-to-day projects. As you get more advanced, you may find that Fusion360 can't do what you need anymore. That's when you switch, and not before. Unless...
2. What CAD system(s) do I need for job qualifications?
If you're concerned mainly about job placement, you'll want to learn one of the big MCAD systems, but it doesn't much matter which. SolidWorks, Creo, and Inventor are all good options for typical ME work, and bonus: they're all pretty much the same thing (duck and cover!). Seriously tho, when you know any one of these three, learning the other two is a cinch.
If you're wanting to design Planes, Trains, and Automobiles, you'll need one of the Big Boys: CATIA or NX, but be prepared: the documentation sucks, and there are very few (good) tutorials out there. Learning will be tough.
Since you're already enjoying F360, I'd probably recommend giving Inventor a spin. It's functionally very similar to all of the other parametric MCAD systems, but does have some limited tie-ins with F360 (being Autodesk and all).
As Josh said, going with job board postings is a good way to go as well. Just keep in mind: CAD is only a tool. Engineers often drive CAD packages, but an Engineer is not a CAD guy!
Let us know what you go with.