The system supports standard (unbuffered =
UDIMM) DDR3 memory modules.
But not all DDR3 memory will be compatible due to the type of memory chips (black squares) used on some of the memory modules.
Here are lists of system compatible DDR3 memory modules -
H71M-DGS motherboard tested memory
Kingston memory from their website
Transcend memory from their website
G.Skill memory from their website
As can be seen, there are quite a few compatible DDR3 memory modules for the H71M-DGS motherboard.
For maximum performance and compatibility, it is suggested that a dual channel kit be bought to replace the existing 4 GB module. The existing 4 GB module could be kept as backup or sold. A dual channel kit contains two memory modules which have been tested for compatibility and guaranteed for compatibility between each other.
Suggest either a 2 x 4 GB dual channel kit, or a 2 x 8 GB dual channel kit. A 2 x 4 GB dual channel kit would probably be sufficient for most tasks and for some gaming as well. But if into video editing, graphics work, heavy gaming etc, then a 2 x 8 GB dual channel kit might be the better choice.
Note that the motherboard supports up to 1333 MHz memory natively without any overclocking. Memory installed that is rated higher than 1333 MHz will automatically be downclocked to 1333 MHz to match system compatibility.