Since you are using Standard Edition, you cant use TDE. So other options are
Using encryption keys at instance/database level :
SQL Server has two kinds of keys: symmetric and asymmetric. Symmetric keys use the same password to encrypt and decrypt data. Asymmetric keys use one password to encrypt data (called the public key) and another to decrypt data (called the private key).
SQL Server has two primary applications for keys: a service master key (SMK) generated on and for a SQL Server instance, and a database master key (DMK) used for a database.
Also, you can have encryption at column level by creating a MASTER KEY ENCRYPTION along with CREATE CERTIFICATE and then CREATE SYMMETRIC KEY.
An example of how this can be done is described at Encrypt a Column of Data
Reference : SQL Server and Database Encryption Keys (Database Engine)
At Drive level :
Using BitLocker as it is a Drive Encryption data protection feature available Windows Server 2008 R2. Refer to : BitLocker Drive Encryption Overview There are many opensource or third party software to do the same job but at additional cost.
Note: The most important bit is ALWAYS backup your encryption keys.
You can use third party software like Redgate's sql backup which allows you to encrypt backups using passwords.
Depending on what level you need encryption will determine if it is worth upgrading to enterprise edition or not. You have to evaluate native TDE encryption vs encryption keys and certificates vs open source vs disk encryption.
PostgreSQL doesn't currently support DB-level encryption. (Correct as of 9.4, at least).
You can use an encrypted file system, though the performance impact can be pretty serious for write-heavy systems, especially those doing random I/O. Your options depend on the operating system - Microsoft BitLocker, Linux's dm-crypt/LUKS/cryptsetup, OS X's FileVault 2, etc.
Alternately, look at PgCrypto for field-level encryption, but beware of key-disclosure issues in logging and pg_stat_activity.
See also:
Best Answer
Backup Encryption was added in SQL Server 2014.
And SQL 2008 R2 is out of support. So upgrade, and yes, otherwise you can use TDE, or write ordinary backups to an encrypted location (eg with BitLocker).