Hi Ben,
I is not a case of which one do you need for Stripe payments. It is more about what domains etc that you want to secure.
Personally, I would not opt for one of the free or cheap and cheerful certs (like 40 bucks).
I would recommend DigiCert as the service was exceptional.
Basically this is my understanding.
Standard SSL Certificates (Single Name) – SSL for a single Domain …. Mycompany.com or www.mycompnay.com - no sub domains
Extended Validation (EV) Certificates - Highest level of authentication – get the Green Bar – Builds trust - no sub domains
Multi-Domain (SANS) Certificates – Multi Root Domain / Multi Server Certificate - no sub domains
Extended Validation (EV) Multi-Domain Certificates – Combo EV and SANS certificate - no sub domains
Wildcard SSL Certificates (Entire Domain) – Secures entire domain including sub-domains