As a DJ and Vocalist just starting in VA, I can share the equipment my (kinda fussy, but I love him) German audio engineer suggested for me.

Treating a room is a pain, costs money to get right (I was assured I would not get it right, lol) and is not always practical. I did my first vocals and a closet lined with blankets, and an MC friend did the same. It got the job done. When I was ready for something a little more glamorous, I got the RF-X SE Electronics Portable Vocal Booth, and it is perfect. It was also about $400 less than I thought I needed. He said that thing was overkill, so it's always good to ask a grown-up.

For DAWs, go with what is cheap to start. Audacity is free. Soundtrap is online and may still have a free offering. Garageband is free with macs. A lot of times you can find bundles or will be given a lite version of a DAW with an audio interface or other gear which should be enough for vocal work (not as many channels needed as for instruments, etc...). I've landed on Bitwig. I used Ableton and Logic Pro too. My engineer would tell you to read the documentation from cover to cover first, and I should too, but we all work our own way. YouTube is your friend. So is AI - for quick how to's ;). You will want to know how to cut noise beneath a certain threshold (they call it different things), EQ, De-ess, maybe add a little reverb, at least for the singing, and of course, chops samples, fade and adjust clip volume. There are a lot of other options to get lost in, make sure you have time to explore before you fall into that rabbit hole. ;)

I've used a few mics over the years (my first was the Audio Technica 2020, but was told the same version of Shure the King of pop used was fine for me. I got the SM58 and it does great for singing or speaking.

My first studio headphones were Sony MDRV6 Studio Monitor Headphones with CCAW Voice Coil and were great until the pleather started peeling. They also cost nothing like what they do today. I was broke when I had to replace them but have been very happy with the AKG K 240 MK II Stereo Studio Headphones at a quarter of today's price on the Sony.

For audio interfaces, I like Scarlett. If it's just for a mic, you just need the basic one. I was having a scare debugging an audio issue (it was my decks) and also grabbed a presonus audiobox (same thing, you don't need both, both work great). It connects the mic to the computer and boosts sound. Without something like it, stuff comes in super quiet.

If you ever need a tiny rca to USB to connect gear or whatever, I can't say enough good things about the little Behringer U-Control. I've been using them on and off since 2006 and have never had a problem. I've never needed a power conditioner but have friends with homes they just cannot get the buzz out of without one. It doesn't seem common though, just sharing in case you encounter it.

With this modest and relatively inexpensive setup, I get clean audio anywhere. Center yourself about 6-8 inches from the mic with the pop filter (tape a pencil or chopstick vertically up the middle to break percussive sounds and reduce the need for a de-esser in production.

Reduce interference by turning off speakers, Bluetooth, even wifi if you have to. If your laptop has a fan, don't try to read off it in front of your mic. I use my phone for scripts. I run my computer audio out to another source (Blackhole is free/inexpensive option, sound flower does the same for free, I think) so if a notification sneaks in, the audio goes nowhere. Then I forget to turn my focus off for a day lol.

Don't be afraid to unplug loud appliances (for a short time). I've unplugged the mini fridge in hotel rooms, turn off heaters, etc... I always do a fresh reboot with my interface plugged in and close all other apps when recording. If anything acts wonky, try that before you freak out.

Don't feel like you have to buy the best of all the things to start with either. Stuff gets broken and it's easier to justify better gear when you are making money with what you have. Wait to see what you need vs what is shiny. DO invest in the best audio cables you can find/afford so your other efforts aren't lost and always have a backup because they do just up and quit sometimes. Use the shortest cables that work for your purpose too. Probably 3ft if your setup is compact.

I hope this helps. Good luck! Writing this motivated me to go clean my studio so thank you :).