Certificate for Security and Connection Servers

Hello there,

I have the below setup

1 Security server - myview.domain.com (mapped to public IP when accessing through the internet)

1 Connection server - myview.domain.com (same FQDN mapped to an internal private IP using local DNS)

So users from inside will resolve the internal IP, where if they leave the company they'll resolve the external IP.

Now the question is, if I generate a certificate from the security server:

1- what type of certificate should I buy from Thawte or DigiCert?

2- Can I import the same certifcate on both Connection and security servers?

Regards,