^^ Sapphire is good but MSI Dual fan version is better and available at the same price.
Koolen, first buy the GPU, check its performance with different games, do some mild overclocking. Once you're familar with all those stuffs, then try overvolting, BIOS modding etc. However, I don't think BIOS mod of HD 6850 will work with a HD 6670.
Listen carefully, BIOS mod only works with same cards of different versions most of the time. For example you can flush the BIOS of a reference HD 6850 with the BIOS of a MSI Cyclone overclocked version of 6850.
In other case BIOS MOD work when a lower level card is basically partially disabled version of a higher end card by using BIOS setting. For example HD 6970 and HD 6950. Some versions of HD 6950 are basically HD 6970 with one shader processor clusters disabled in BIOS. Here BIOS mod of a HD 6970 into a HD 6950 can unlock the later one to the former one.
In your case, since HD 6670 is not the shader disabled version of any higher end cards, you can only try with the 1st option. But first get accustomed with overclocking and then go for that.