Do I need to start a publishing company and purchase ISBN’s in order to succeed?

For whether or not you should purchase ISBN numbers, read the “Should I purchase ISBNs or should I use the free CreateSpace ISBNs?” question here in the FAQ. Basically, if you live in Canada or plan on printing anywhere other than CreateSpace, you should get them, otherwise it's basically for vanity. Which is a very valid reason for purchasing your own, but John & Jay don't see the need and I haven't gotten around to it yet for my own publishing company despite wanting to remove CreateSpace as the publisher for my books.

As for forming your own company, I highly recommend it. It lends a lot of credibility for landing clients, it can help protect your assets and limit your liability (it's worth spending the money to have an attorney set you up in my opinion) and it can give you a “home base” for promoting all of your client's work. You don't need ISBNs to start a publishing company; so I'd recommend waiting until you have sufficient cashflow to purchase them if that's something that you decide to do.