DSC H1 telephoto lens help required

Hi - I am new to the forum and photography and am seeking information regarding an apropriate telephoto lens for a Sony cybershot DSC-H1. I would like a genuine sony lens in an attempt to maximise image quality and have identified two possible options.

1. VCL-DH1758 - Specific to the DSC-H1
2. VCL-HG1758 - More expensive, larger objective lens.

Both have the necessary 58mm thread but would the larger objective lens of the HG1758 give better results? Would any sony lens with a 58mm thread work on this camera? Any thoughts or experiences would be appreciated as I am hoping to achieve results as good as possible on a limited budget.Thanks.