Hey, welcome to RO, this is my favorite audio site cuz the community is realityivly small, and the regulars are really very helpful.

So what floor are you on, where else are your neighbors?

Bathrooms are usually larger and more odd shaped than closets, so an average clean b room w some budget quilted blankets hanging around your area, would be a decent place to start w something like this.

I would pick that over a closet to start, because of the size, and really the availability of maybe some tile or whatever to not over kill the vocal. W a condenser I'd start on the deader side, and move the absorbstion further out, and balance life of sound w intimacy.

Basically, the level of isolation you, err your neighbors, want, is very very expensive. A pro level room can range from 50 to well over 150 per sqf.

But thankfully your recording a soft source, but, you need to feel comfy to open up.

Cheap isolation is using headphones, and singing when others aren't around.

There are two things you should research around here in the acoustics area, acoustics, and isolation. Acoustics is the way the room responds to sound, as in boxy, or bright, or dead, ect. Isolation is how quiet it is inside and out of your room.

But really man, your lucky if it's just vocals, cuz it's a close mic'd, fairly not loud sound. Your mic figures into it too. But a few quilted moving blankets, there blue, and about 50 for a 3pack, some masking tape can give you a reasonable area.

It is a good idea to get a 10$ bottle of fabric fire treatment spray, and comply to all local codes.

I don't know what you read but, it was bs. There are books that tackle what yr talking about, and honestly the starter for you, I think, could be acoustic design for the home studio, by Mitch Gallagher. While it's not my fave and I don't agree w everything, it's 101 for the basics, and guerrilla stuff. Rod Gervais, home studio build it like the pros, is the one when the guerrilla stuff doesn't satisfy, and money plus some carpentry skill can, and will help you. The more theoretic based offerings are from Alton Everest, and Phillip newel.

There are no recommendations for the use of mattresses, or closets, in the ones I've read.

It really depends on your budget/expectations, as to whether is old clothes duk taped to walls, or nice little DIY panels, or a dedicated room. Keep it simple. These things get way way out of hand sometimes.

If you have a hundred, budget for three, ditto for hours of labor. I like the idea of some fiberglass panels hanging from a few budget mic stands.

So it seems like you rent space within someone's home? Or is it an apartment? Either way, items that absorb sound, DO NOT prevent sound from traveling through to your neighbors. I have worked and built many studios and sound absorbing products is just that...it stops sound from bouncing around but does NOT prevent sound from being heard through the tiniest cracks. Don't want you to waste your time or money. If they can deal with minimal noise, then you can try creating an ISO booth in your closet or bathroom...but it won't be sound proof, especially if you are a loud singer.

My suggestions: Perhaps try renting an hour or two from a local rehearsal space, and save yourself the time, and worry that the neighbors will hear you. You can do monthly plans, and shouldn't be more than $10-15 an hour in most places.

next suggestion, is to see if you can have a carpenter or contractor build you a small portable booth that you can set up and take down easily...it's a less expensive alternative to buying a whisper room of sorts...but you may be able to score one for about $500 or less used...gotta look around. Hope this helps you.

You really shouldn't have problems practicing your vocals during normal business hours. Most all jurisdictions have some kind of noise ordinances, from generally between 10 AM to 10 PM.
If the neighbor next door has an infant? Your results may vary? Are you a screamer? Or opera singer? Do you sing Mozart or Black Sabbath? That could be a factor?

A mattress? You must be kidding? Mattresses are for sleeping. You might stick one between a drum set and a guitar amplifier if you want to get some sleep? The only way to prevent noise transmission is to build a shock mounted, spring-loaded, rubber foot damped room, within a room. Air transmits sound. So you've got to seal your self up. (Oxygen tanks and masks optional) And you really can't do that in a rental, no.

You can however build or purchase a vocal booth. Not my 1st choice but... if you've got to? Ya got to. I've used vocal Booths like that and they sounded just fine. Not the sound I like but obviously, usable, adequate, better than not having it. No choice, choice. Vocals could have sounded better in a larger room but... that wasn't an option. It's not a deal or a hit, killer.

This is not exactly an inexpensive project. It has to have an air supply and circulation. It has to be a box. You'll have to schlep it in and assemble it yourself as it is modular. And you're not going to be jumping around. No. So that's the compromise you're going to have to make. So... I don't much like vocals in booths. But in the past, sometimes you don't have a choice. But it's not horrible or unusable. It's adequate. Just don't use too much foam thingies. Particularly if you build up your own box from scratch.

I mean if you think your material might be hit material? You might just do all of your production in the computer and then go to a local studio to cut your vocals? That wouldn't be terrible especially if you are well rehearsed. But if you take 10 hours to sing one song? Likely not practical? And if you can't get a song down in 3 takes? Go on to the next song and come back to that one later. That's the practical way to go.

Apartments are tough.
Mx. Remy Ann David