@Alexander Friedman,
The reality is that there is not a single right way to get started. I purchased my first property 2 years ago, using a number of credit cards (I did pay for a service to help me get the credit to begin with). Now that I have quite a few rental units, I've been considering going for my license, and focusing on the commercial side of the business, as working with investors has more appeal to me than working with first time home buyers.
The question you may want to ask yourself: what will help you get closer to your goal? What types of networking will help you gain the connections with people that are doing what you would like to be doing? Your day job may provide some of those opportunities, especially if you let all of your sales prospects know that you are interested in investment properties.
Finally, to address your original question: it's possible that a principle broker may not be excited that you're an investor, if you're not planning to bring in additional business. They may be worried that you would have a complaint filed by a tenant or someone that you'd purchased a below market house from. Not all principle brokers will mind, although I've been told this by a principal broker recently.