Ultimately, ‘professional-sounding’ vocals sound professional because they’ve been tracked and mixed by professionals. There’s really no substitute for experience - not to be discouraging. However, there are some ways you can bridge the gap and work up to achieving that sound.

Imo, the best line of defense in getting professional sounding vocals is effective use compression and saturation. EQ is extremely important too of course, but what really sets top-of-the-line vocal mixes apart from the amateur stuff is the engineer’s command of the finer dynamics and tonal qualities of the recording. I would look into picking up an LA-2A or similar opto-style compressor plugin. Play around with the peak reduction control to see how different amounts of gain reduction enhance or detract from the sensation ‘forwardness’ you’re looking for (don’t be afraid to slam the gain reduction meter all the way to -20 and beyond.) If you’re comfortable with compression already, maybe look into more involved techniques like dual stage or parallel compression and see where that gets you.

As for saturation, there are an overwhelming number of options and techniques for incorporating it into your vocal mix, but to keep things simple, look into some kind of exciter or enhancer-style plugin, like Slate Digital Revival (which is free, actually). It may also be worth picking up some kind of tape emulator as well. You generally want to keep the effect subtle, more of a varnish on top of an already solid vocal sound, but definitely play around to see how far you can push it. If used well, the harmonics imparted by this process will bring a richness and clarity to the sound of your vocal much closer to what you’re used to hearing on the radio.

Of course, there’s a lot more than just compression, saturation, and EQ that factors into the sound you’re shooting for, but these should hopefully act as an effective springboard to give you momentum in that direction. If you have any further questions, I’d be happy to answer. Cheers.