That is an excellent question, Cody, and the answer is going to depend on a lot of things:
1) Your circumstances. When my full time job ended at the Community College (the federal grand funding ended, so did the position), I decided that full time work for someone else was not what I wanted. I did not have a family to support, I was within 10 years of retirement, and I preferred being an entrepreneur. Had my circumstances been different (younger, with a family) I might have made a different choice.
2) Your financial situation. Do you have the finances available to support you while looking for a full time job? I did not, so when I started my own business it was with the intention of bringing in some income right away. It worked - I am self-employed, with enough work to support me and, as it turned out, my daughter and her family when they fell on hard times and had to move back home.
3) Your desire to be an entrepreneur. Do you have what it takes to start your own business? Marketing is going to be key. Can you drive customers to your business? My business is online and I am using my experience as a trainer, writer, and editor to provide the creative side of the business. I also have a degree in Business Management to provide the business side of the business.
4) As for the stock market question, I am sorry, but I don't play there - too much risk for me. If you are younger, then yes, I would agree that money in the market that you can afford to put away and forget about is a good way to at least partially fund your future. But, I don't recommend anyone putting all their eggs in one basket -- diversify if you are going that route.