What equipment and software are essential in your home studio setup?

 Both my USB Rode NT1 5th Gen (for travel) and my in-studio Rode NT1

My Steinburg UR12 interface

Adobe Audition DAW (digital audio workstation)

Blaze computer backup service (never want to lose precious files and data!)

Quality plug-ins for de-noising audio created in rooms with poor acoustic value

Short and sweet answer:

Acoustic room (sound-treated for noise cancellation purposes)

Computer

Audio interface

Audio editing software

Good condenser microphone

Mic stand with pop filter

Studio headphones for monitoring audio

That depends on what you are looking for as a result...
The ESSENTIAL is:
Just a laptop with any DAW (Logic, Pro Tools, Live, etc..), a headphone and you are good to go.
If you are something in the means of an electronic music or hip-hop producer that will suffice for you.

If you are a guitarist, you will need an interface to plug your instrument and play it through the DAW with some amp simulation.:

If you are a vocalist, you will also need a good mic... I recommend an sm7b with a Dynamite pre amp by SE Electronics... or just an Sm7db...

Additional gear, such as MIDI controllers, pedals, etc., can also be good to make you more creative. 

Don't waste good money on bad cables and accessories, go straight to trusty brands such as Monster, Mogami, and others...
 

My first suggestion would be to invest some money to correct your room acoustic: expensive monitors or hardware interfaces will not save your works if the acoustic of your room is not working properly. Then, once treated the room correctly, get two good speakers (and a subwoofer if your acoustic is really fine) and an audio interface with good converters.

Put as simply as possible:

• Microphone: Do some research into what other VO artists recommend. There are thousands to choose from, but a few are notable in the industry.
• Audio Interface (also referred to as a sound card): This is a small box that you will route your XLR microphone into. Use it to control the gain and phantom power of your mic.
• Computer/Laptop: You need to record into something!
• DAW/Workstation: Again, many to choose from. Many beginners use Audacity although it's features are limited. Others include Cubase, Logic, Ableton and Pro Tools.
• Recording Space: You need a treated space to record in. No ifs, no buts - this is the basis of the quality of your recording. If your recording space is poor, your recording will be poor.

If the purpose of the studio is strictly Voice Over, then I would suggest - 

• Small capsule shotgun mic - shotgun mics like the 416 help reduce reverb and slap in a moderately treated room.
• NO USB MICS! - sure they are cheap on Amazon, and maybe someone told you they make tons of money using a USB mic for pro VO work, but it's likely they lied, and large paying VO jobs require high end mic and interfaces.
• Audio interface - the Focusrite Red series are affordable and fairly decent for a small VO home studio setup.  A serious upgrade would be the UAD interfaces and up from there.  Yes you will hear the difference if you upgrade and have good monitoring......
• Good monitoring - for VO look a the Genelec 8020s - sure a bit pricey buy many dialog editing suites in studios use these and they have a small footprint
• Room treatment is a must.  There are plenty of YT videos on this, but please do not use foam from Guitar Center, it's just overpriced junk.  Look at some DIY sound treatment videos and with a little effort, you can improve the way your recording space sounds without breaking the budget. 
• El Gato Streamdeck - program in all the hotkeys you use and other functions to work lightning fast when editing and recording yourself.  Time is money and the StreamDeck is a time saver worth every penny. 

I'm going to say something different than the usual advice. 
When your recording environment is not ideal (which probably is the case when you read this question) DON'T get the most expensive gear.

For instance you may want to go and get a condensor microphone. 
However these microphones are quite sensitive and pick up on every little thing in your room.
So if you don't have a well treated vocal booth, you'll end up with roomy, recordings.
Get a dynamic microphone instead, these record only whats close to them, and are much easier to handle. A lot of pro recordings are done with the really affordable sm57 microphone.
Pair that with an affordable interface like a focusrite, and a pop-filter and you're already mostly set for your vocals.

You also don't want to do audio monitoring on speakers in your untreated room. For instance your room may reflect a lot more bass frequencies so you'll hear those a lot louder. Then you may think I have to turn my bass down in a mix, only to hear it somewhere else, and hearing no bass in your song.
You're better of getting a good pair of headphones, closed back so you can also use these to record with. For instance the "Audio Technica ATH-M50x"  is one of my affordable goto's.

Getting your room treated acoustically should come first, before getting expensive gear. You can look up some videos on "DIY Broadband absorbers" these absorb all frequencies equally and are a good first step in treating your room. You can make them yourself quite affordably with rockwool.

TLDR:
Treat your room acoustically first, or get a dynamic microphone "Shure sm57", paired with an interface "Focusrite" and a good pair of closed back headphones "Audio Technica ATH M-50X"

It might surprise you to know that you dont need much to get a great sounding demo together. Depending on your budget you could spend anywhere between $400 and $10,000 and end up with results which aren't a million miles from each other.

Things you will need:
A Condenser Microphone - On a budget look at the Rode Nt2a, more of a budget look at something like a Neumann TLM103. Dont forget the pop shield for it though!
An Interface - UAD are killer for home studios and come with some nice software plugins too, but if the budget won't stretch, check out something from Focusrite.
Some reasonable speakers or headphones - Want to vibe? Check out the KRK Rokits Want accuracy - Yamaha HS5/10s. Or for headphones - check out the DT990Pros which are industry staples 
Software to record into - I personally use Logic but there are plenty of options. You can even use online software like band lab for free!

My thoughts on this are that if you can't drive, you probably dont need a ferrari! Learn to use what you have, and then work out what you want to upgrade when you know what the weaknesses in your systems are. You'll be surprised how well good audio equipment holds its value, so selling equipment second hand to buy more isnt a bad option.

Any questions, reach out!