Personal account -- getting on the share register

Hi this is a question for those of you running personal accounts on the side.

At the moment all I want to do is buy a certain company's stock, and hold it for the forseeable future (long term). However I want to be sure that I am on the company's share register. Is this possible through a normal discount brokerage account? Would the stock certificates need to be made out in my name, and would I need to physically hold those certificates (or could I still let the broker handle all of that, without having to forgo any of the benefits of being a registered shareholder)? Just looking for the most cost-effective way (yet still compliant given that I work in the industry) to get on the company share register. Not sure what specifically to ask for since I'm new to brokerage accounts.

Ideas and suggestions welcome, I know very little about equities.

Thanks