If you take a look at a handful of product manager job descriptions, you will soon realize how diverse the role is depending on the vertical as well as company-specific challenges and priorities; therefore it is not easy to pinpoint the exact characteristics of s successful product manager. I will try my best to keep it as generic as possible from having my own startups and working for both small and big corporations.

Qualitative Skills:

• Empathy: by far, this is the most important character of a PM in my opinion; it might not sound intuitive, but no matter how good you are in your role, without authentic human interaction you will fail to deliver a successful product. This is specially the case for PMs as you are technically no-one’s boss and have to rally your teams behind a vision without much formal authority.
• Curiosity: every successful product once had a curious mind behind it; in order to stay competitive, you need to establish a frequent communication channel with users and couple the qualitative data that you gather with data to make sound judgement and solve problems. Another part of being curious is utilizing a scientific approach for testing to validate your thoughts. You would want to closely “spy” on you direct competition and watch for indirect, potential, and substitute ones.
• Communication. Product Managers are the “glue” between business and technical side of a product; what this means is that you need to establish trust with all stakeholders and be transparent in your correspondences. In order to be an effective communicator you will need to first know your audience and their communication style and second talk in their own KPI. My favorite quote is “You can’t bait a fish with a strawberry!”.

Quantitative Skills:

• Prioritization: As the product chief, all will always have requests coming in from internal and external stakeholders and the reality is you have to be able to methodologically prioritize and say “no” to the ones that aren’t aligned with the product vision. So it is crucial to cut through the noise and focus on the features that are important to the users and company. No you might ask how do I even go about prioritizing all the noise? This is why frameworks are built to help guide you along the way; my favorite one is User Mapping framework by Jeff Patton. User Mapping is widely adopted since its inception in 2005 and you can utilize it for both product feature and roadmapping. 
• Data-driven decision making:  as they say “nothing beats data” and there is certainly a lot of truth to that. Data is what gives you confidence in your day-to-day decision making as a Product Manager; however you need to establish metrics for your data and those metrics need to be communicated and agreed upon across an organization. It is more so important in testing your hypothesis with a MVP; you need to know what does success look like before running any tests. As a rule of thumb, good metrics are understandable and are in the rate/ratio format.