First, measure most everything at the day, week, month and yearly level, then do week over week, month over month and year over year comparisons. Usually this means we store the most granular level and then rollup from there.
What to measure depends on what you are doing, but IMO these are some general things you should always measure: signups, cancels, time on site, time from signup to first use, A/B tests of course on features, pricing etc. This is in addition to the normal reliability, server metrics etc. I recently setup our sites to start tracking peoples first visit until signup, of course this isn't foolproof as it relies on a cookie, but I think it will help us over time.
The key to the analytics/metrics is you want to be able to cross section them and be able to look at when you add a new feature, or remove something etc.
Frankly, besides storing normal metrics, we store every API call, the time it takes, who made it, which machines were involved etc. This lets us basically look at everything that happens. From that I can get signups, cancellations, engagement statistics and a whole host of other things, this solves most of the business questions and almost all operational concerns like machines being whacked.
Not saying my ideas are 100% right or even correct in all circumstances, but thought I'd at least share.
From the business you need to measure profitability, cash, revenue, customer acquisition cost, supply chain (where the customer came from), customer value, life time customer value, time to cover CAC etc. Not sure where you are at with those.
Even in these broad categories there are lots of details. For example on revenue, IMO you should measure it against head count, as well measure profitability against # of employees etc. When you are bootstrapped or working on the smallest possible budget, this will also help you know when you can/should add more staff etc.
Hopefully that helps a little. Let me know if I can help you any more, happy to share whatever I can.