I have to respectfully disagree with the first line of this. Startups biggest competitive advantage is productivity (theoretically they will be more agile, have less bureaucracy, etc), and productivity is largely about time management!
As a first time founder myself, I can agree that the amount of tasks that get thrown your way can be horrendous. Especially if you, like me, were used to being a developer where it was often encouraged that people not fuck with you for a solid 4-5 hours so you can do your thing.
I've started by taking advantage of to-do lists. I had always used them to some degree, but now I put EVERYTHING on my lists, and am constantly evaluating the priority. Most recently I've been using Trello (Kanban).
I can't really give you advice for the priorities because that really depends on your business, who you have working with you, and a number of other factors.
Additionally, this may not be applicable for you, but I have to block off a certain time of day to code. It isn't always the same time. It fluctuates from 430AM - 1030AM, to 9PM - 3AM. It isn't regular at all. But during that time I know coding is the ONLY thing I will address.
I block off my coding time because for me, it is the least unpredictable. I cannot predict what sort of customer support, deal work, or an infinite other amount of phone calls will come up. So the easiest way to handle it, for me, is to know that I have a certain part of my day (very early or very late) dedicated to code, and the operational issues and customer support can be handled in the middle.
My hardest problem has been feeling like the items I tackled that day were the right ones. I often go to sleep feeling like I should have focused on something more, and other things less. I suppose that is normal -- there is always room for improvement.