There are really several ways to have "something of your own", so you will have to define exactly what that means to you in order to get any meaningful help.
I've literally never had a full time job as an employee for anyone, all of my jobs have been self employed and they've all been so wildly different, I can't draw much of a commonality.
For example, I was self employed, but worked as an independent contractor in a role that was very similar to being an employee. But technically I was.self employed.
At any point I could have purchased the business I was contracting for or partnered with the existing owner. I didn't want to because it was not a business model that I wanted to be leveraged in.
I had multiple consulting side gigs, which were also self employment, but more independent than the main contract gig, so I really wasn't reporting to anyone.
My family own brick and mortar retail businesses, and my mom was a dog breeder and a management consultant. In addition, my brother is a photographer, a cousin owned a paint store, a few family members are writers, one owns a vegan protein supplement company, another owns a speaker company, and another owns tons of real estate, two of my exes own small software companies, another is a filmmaker, another is a partner in a law firm, another co-owns hospitals, and a dear friend owns a bunch of religious websites. This insane range of self employment all falls under the umbrella of "having something of their own"
The world of "having something of your own" is actually broader in scope than the world of being an employee. There's way more range and possibility.
You need to narrow down though the key factors of self employment that you are looking for.
The main benefits of self employment are:
-greater autonomy
-full ownership of the profits
These can both be pros and cons. Full autonomy also means full responsibility, which really is a double edged sword.
Full ownership of the profits also means full ownership of the expenses and losses. Remember how I said I avoided ownership in my industry? This is because after the business loan costs and overhead, I was taking home over double what the owner was and I was working part time.
So first narrow down what you are looking to gain from having "something of your own" and then work from there to find something that can meet your goals.
From there, you need to figure out if you want to capitalize on a professional skill you already have, or break into a totally new line of business.