I, too, was a mechanical engineer out of school, and have always been pretty entrepreneurial. I'm now the founder of LoyolyPRO, and have 3 kids and a mortgage. As with all the advice you get here (including, and especially, mine) read it, digest it, and then figure out what is important to you.
There are MANY pros of starting your own company out of school, and also many cons. BUT, there are many pros and cons with waiting. There isn't a right answer. Let me try and detail some of the important things that you want to consider.
Starting a company now:
1) You don't know any better, and so you aren't hung up on things that others tell you you can't or shouldn't do. You will just do it.
2) You are young. You can live with your parents. You don't need lots of money today. (This becomes a problem when you have kids and a mortgage.)
3) You have energy...lots of it.
4) You will likely fail. You will get battle wounds. You will survive. You will learn from your mistakes. You will take another shot, and you might succeed. Or maybe not. But you will take another shot. There is no way you can learn as much as quickly as if you were working at someone else's company. It's a brutal journey, but you will be better for it.
5) When you go work for someone else's company, they will pay you fairly well, and complacency sets in. There is more at stake for taking the leap, and you might not.
6) You will get married. Your wife will provide many reasons not to do it. A steady paycheck is a wonderful thing.
Starting your own company later:
1) It's good to learn and make mistakes on someone else's dime.
2) Becoming an expert in something is important. Figure out what you like to do and become an expert. That will give you many ideas on what to do in the future.
3) You will meet people and build connections. Starting your own business is a lonely venture. You can meet some amazing people that will help you along your way.
4) Starting a business with a steady paycheck is a good way to go. Only once you get going sufficiently do you need to make the leap and go full time.
5) You can save some money. This is REALLY important. One of the biggest challenges new companies face is under capitalization. Making sure you have sufficient money to fight your fight is important, and allows you sufficient runway to make mistakes and continue to revenue.
Hope this helps!