The E2160 is a 65w CPU, and the Radeon 6670 is a 66w GPU. Theoretically, your 300w PSU could power that combination.
However, if you are going to get an inexpensive PSU, I was going to recommend the model that you linked to. The good thing about quality PSUs however is that you can carry them over to your next build. Think of it as a capital investment and it won't sting as bad...
For a system using a single Radeon HD 6670 graphics card AMD specifies a minimum of a 400 Watt or greater system power supply. The power supply should also have a maximum combined +12 Volt continuous current rating of 19 Amps or greater.
Total Power Supply Wattage is NOT the crucial factor in power supply selection!!! Sufficient Total Combined Continuous Power/Current Available on the +12V Rail(s) rated at 45°C - 50°C ambient temperature, is the most critical factor.
Overclocking of the CPU and/or GPU(s) will require an additional increase to the maximum combined +12 Volt continuous current ratings, recommended above, to meet the increase in power required for the overclock. The additional amount required will depend on the magnitude of the overclock being attempted.
You may find power supplies on the market that supply more than enough Wattage to run the system. However, some of them lack Sufficient Amperage capacity on the critical +12 Volt rail, which is necessary to properly power the critical components in the system (i.e. CPU and GPUs). This is the reason why graphics card manufacturers may overstate the power supply wattage, usually by at least 50 Watts, in an attempt to take into account some of those power supplies that have the weaker +12 Volt rail(s).
The HP 404795-001 300W power supply (Lite-On PS-6301-9), with its maximum combined +12 Volt continuous current rating of 18 Amps is borderline insufficient to power your system configuration with a single Radeon HD 6670 graphics card.
ko888, I am now trading this system in for a slightly better one. I will find out what the PSU is on Wednesday. I will ask for PSU advice again for the less-dumpy system, it sounds like I might have to that CX430.