In my opinion, given the information you provided, the SAQ A-EP fits your scenario.
You are not self hosted and Digital Ocean is your third party provider. Hosting is more than the software you host but also the physical security of the hardware. Digital Ocean likely have access to your data stored on the server, and could alter files on the box that cause the payment pages to change without SSH access. Regardless of whether it classes as shared hosting Digital Ocean still need to be validated to the relevant items of PCI DSS (see below).
I don't know if they would be classed as Shared Hosting though and I'd rely on advice from a QSA on this one. If its not Shared Hosting, get clear justification for why.
In regards to segmentation, most companies will have parts of their systems in-scope and part out of scope. The parts in scope should be segmented and controlled from the parts out of scope. You may wish to make your entire website in scope, or you might wish to break it up into seperately hosted parts. External parties may fall in/out of scope too. e.g. Digital Ocean will be in scope, but the Internet will be out of scope. Secure your in-scope environment using firewalls and other means, so only the traffic intended to and from your environment is allowed.
The SAQ A-EP requires several things in the 'Before You Begin' section that will all be things you should check. A couple I want to call out, that sound real relevant to the questions you're asking:
Your hosting provider needs to be validated to all applicable PCI DSS requirements
If merchant website is hosted by a third-party provider, the provider is validated to all applicable PCI DSS requirements
Digital Ocean essentially needs to be PCI Compliant, or to some of the requirements at least, for you to be PCI Compliant. Last I checked they aren't. AWS has maintained PCI Compliance for sometime though, and they are a good default for virtualization and PCI.
Don't use external JS, CSS, etc on your pages using StripeJS
All elements of payment pages that are delivered to the consumer’s browser originate from either
the merchant’s website or a PCI DSS compliant service provider(s);
It's your responsibility to make sure your service providers are PCI compliant
Your company has confirmed that all third party(s) handling storage, processing, and/or transmission of cardholder data are PCI DSS compliant
The above is my opinion and not advice, you should not rely on it, and instead consult a registered PCI QSA for advice. Block quotes are from PCI DSS SAQ A-EP v3. Always read the full SAQ and PCI DSS.