I'm going to mostly disagree with pp's advice (sorry) 
The top review of the recommended book is a 1 star which says the book is well out of date and doesn't even mention kindle???
I'm baffled.
Not at PP of course, more that 'they' have the audacity to keep selling the book?! 
Op... self publishing is as easy as paying someone $10 on Upwork to format your book and pressing maybe 5 buttons, or as complicated as having a PA to manage releases, a designer on retainer, a team of proofreaders and someone to personally manage your facebook ads.
What do you want to achieve?
If it's mainly about prestige and you're doing this for you, find an agent.
If it's not about prestige, and you're either doing this for you or you want to make money / start a career, self publish all the way. Take the time to learn about it like you would any new venture.
If you just want to publish a book to say you've published a book, it really is very simple. Find a freelancer to format (Upwork, Fiverr etc) which is about the only technically complex part of it... and either make your own cover on kindle create (or an app like canva) or again, pay someone $30-$50 on Fiverr to do it for you. I used GermanCreative there for my first cover and that book has made thousands. I've also used a homemade Canva cover in my early days and the book passed five figures within a couple of months. I then recovered because I had the money, but when you don't have the money you do what you can with what you have.
Proofreading is fairly easy to find, and again, you generally get what you pay for. I've used people overseas and the results were fine for the genre. I now use an American friend who is excellent and I'm yet to find an error in any of her manuscripts, I use her for book 1s in a new series. In the past I've done it myself using grammarly / pro writing aid and text-to-speech.
If you want to try to make money, try to start a career, try to get people reading your work etc then first, join the Facebook group 20booksto50k and absorb everything in the modules. Familiarise yourself with the KDP interface.
Then you'll need to work out if your book is written to market, and if it's not, brainstorm ways to see if you can make it more 'to market'.
Once you've honed in on a potential market, study the covers and the titles and the authors already dominating, and what they're doing to dominate.
Don't publish until you're as confident as you want to be that your book has potential readers and everything about the book (cover, title(s), blurb, keywords, in that order) signals you have exactly what those readers are looking for.
How much you spend on the process is almost entirely up to you. Active marketing will cost money ($5 a day facebook ad can be enough for the right book, $40-$100 newsletters in certain genres) unless you are writing in a genre with a big social media presence, in which case join readers groups and engage. Passive marketing (cover, title, blurb, keywords) is free. Covers range from $5 for text slapped over an image to $500 for a high (but not top) tier Urban Fantasy.
It boils down to want you want to achieve. If that's seeing your name on a book and holding that book in your hands, it won't really cost anything.
He has paid for some of the publishing, and the publisher does all the leg work to get it published and promoted.
This sounds exactly like vanity publishing. Op, if people want you to pay them to publish your book, run for the hills. Don't even engage.