How to Get Radio-Ready Vocals at Home: A Checklist

The checklist

Record clean. Close mic, pop filter, quiet room, level peaking around −12 to −6 dBFS.
Clean up. Remove noise and echo, then fix clicks and pops. See the guide on removing echo.
Shape the tone. High-pass, then cut mud, then lift presence, then de-ess.
Control the level. Compress gently so every word is heard.
Add space. Short reverb and delay on sends.
Balance with the beat. See mixing vocals on a beat.
Check loudness. Measure with the LUFS meter and listen on a phone, earphones and a car or laptop.

Radio-ready also depends on the song and the performance. A good chain on a weak take will still sound weak. Re-record the parts that need it.

Spot clipping, noise, rumble and level problems. Runs in your browser, nothing is uploaded.

Do I need expensive gear?

No. A clean take on a modest mic in a quiet room beats a noisy take on expensive gear.

What should I check last?

The loudness and the balance on three different speakers.

Can software replace a good take?

It helps, but it cannot add a performance that was not recorded.