I'm working at a start-up, and a first PMM hire; what KPIs should I own and not own?

First and foremost, don't commit to any metrics until you really understand the current customer, buying cycle, and GTM approach, and have a point of view on what needs to change. I'm making a few assumptions here that as a "first in" you're further along on your career journey and have a sense of where to start. (If that's not the case, quickly find someone through your VC who can provide some advice here relevant to your problem! First PMM problems are often more qualitative. Who's the real customer? How do we get to her? Why does she care about the problem we solve and our unique solution? But, there's always a way to measure impact of that. Some thoughts here, broken down by the usual "how do you capture revenue?" framework:

• Product-led growth: Trials started, Trials converted, Average Deal Size. The first two are straightforward (and shared with Demand), but critical to see "who's buying" and if they match your theoretical ideal customer profile. Average Deal size links to the PMM objective of increasing the value you capture from every customer.
• Sales-led growth: Demo requests, New Meetings Set, Opps Created. You're trying to learn who is interested, who takes action, and who you ultimately need to qualify into. These will tell you that pretty quickly (and if you have a disconnect in your path from consideration to sale).

Importantly, all these metrics will help YOU improve messaging and positioning. You're learning quickly who is engaging, who you really want to engage with, and if you have any non-personas (targets to avoid) or hidden personas (people you really should be talking to) in the mix already.