Well, you certainly don’t have to go to the airlines, although there are a lot of good reasons to do so.
You have the basic order correct. Train for your PPL, Instrument rating, Commercial License and Multi-Engine rating. This is all pretty expensive because you are paying for every hour you put in your logbook until you have your Commercial license. If you are currently employed then you could chip away at this during weekends/evenings/vacation time and try to pay as you go. This is what I did because I wanted to keep the debt level down. It takes awhile though.
There are fast track ways if you are prepared to pay the money. I have two friends who went through the ATP Flight School Career program back in the early 2000’s. They both have successful careers flying business jets.
There are other fast track schools out there, but make sure you do your homework before making the financial commitment.
I can’t tell you much about the recruitment process at the airlines but I am sure @smokinhole, @Bogusheadbox, @Troll and @Cygon_Parrot could tell you what you need to know.
Business aviation can be tricky to get into as, to a greater extent, it really helps if you know someone on the inside. Networking is key. I got my first flying job because I already worked for the company as a Line Service Technician. When I was flying as an independent contractor (after being laid off during the recession), it was the people I knew that helped me find work when it was scarce. And finally, the job I have now came about because I knew the lead pilot from playing iEN’s Warbirds years before. So, it really does have a degree of luck attached to it. Of course, you have to work hard for it too, play well with others and never burn bridges if you can avoid it.
Pay wise, it used to be that a Regional FO in their first year or two were very poorly compensated. That is improving now though. In the long run, an airline career will most likely result in a better schedule with better benefits and definitely a better retirement plan. It is IMHO too late for me to make the switch at this point. I can’t complain though. I make a good living, have flown some great airplanes, visited places I never imagined I would ever see (and have enough time when there to actually see things) and I work with a small group of outstanding people. So there are pros and cons.
There are lots of other rewarding career paths though. Take a look at what @BeachAV8R does for a living. That’s where it’s at if you want a job flying where you can use your flying skills to make a real difference in people’s lives when they need it most.