Typically for low volume sending it doesn't matter. For high-volume sending you need to get the IPs, domains, and security controls set up correctly to reduce how much you're seen as spam.
AWS SES will allow you to configure this all, but you need to know how. Something like SendGrid (not a small player) will be more expensive, but will provide usability features on top and guide you through that setup of that solid foundation a little more.
Ultimately the reputation comes down to the organisation authoring the email (not the email service provider), as they are the ones doing well or badly on the quality of the email they send.
So yes, own the IP [and do all the regular SPF, DKIM and such], but be aware that is possibly nowhere near enough.