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.
Best Answer
There are 3rd party tools which replicate TDE functionality.
I have tested the following during an exercise to evaluate whether we can move from Enterprise to Standard Edition:
In both cases, they seem to work by placing a driver between the SQL binaries and the storage layer, and after configuration are transparent to the connecting application. Queries work in the exact same way as for TDE-enabled databases. Once the data leaves the storage, it is unencrypted. It would appear as an unencrypted database to all authenticated connections.
They do cost, but I believe there are trial versions available.
In performance tests (10,000 small insert queries into a clustered index) I found that DBDefence closely mirrored the performance of a TDE-enabled database. Query times for Netlib increased by approx 8%. Obviously your specific scenario may differ.
All my tests were performed on SQL 2016 Standard.