Once I've started a business, what's the one/best thing I should do to land my first client?
If you are going to start a business, getting your first client should be no problem assuming that you have a done some sort of validation of your business idea.
In doing that validation you most likely found that there was a need/opportunity to sell your widget. So I would start there. What is the need and opportunity, why do you think the widget your selling is valuable and more importantly - who will find it valuable?
Then, as stated earlier, start with your personal network. Let them know about your new business and ask if they can refer someone that can benefit from what you're selling.
You should be able to get your first few clients this way. The quality of your product/service will give you a platform of growth from there. Make sure to learn and iterate fast from your early customers.