The answer to the question of "to reinvest or not to reinvest" is simple: reinvest!
That is, reinvest as much as you can to keep the business profitable for yourself: if your online business is your sole source of income, reinvesting all of your money is not a good idea. But if you're starting your online business in addition to a day job, definitely reinvest as much of the profits as you can into improving your business.
The logic behind this is simple: the more money you put into your business, the faster it can start to grow. If you improve your website server or pay for a new commerce system or redesign, you can improve your customer's experience at your site, which makes them more likely to buy your product and improve your business. If you refine the product itself, then you make it more attractive to customers and boost sales even more. (It may even lead to a new idea or an expanded product line down the road.)
Taking the profits for yourself beyond your basic expenses is an attractive option, of course – and usually the reason we go into business in the first place. But putting the money you make back into your business allows you to make more money historically, to increase your overall profits, and to keep your customers coming back, extending the life of your business significantly and keeping the revenue stream steady. A central tenet of modern capitalism is that if your business is not growing, it's failing: make sure that your business grows by putting as much money back into it as you can.