No, having a contact form will not use a significant amount of bandwidth, usually less than a kilobyte. As for linking to your email address, you could, but it would be wise to have spam filters on it. Robots will likely scan your page for your email then flood you with spams once your address gets into their database.
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Will using this form in my site mean more costs with regards hosting?
Is this contact form a good idea at all? Or would a simpe link to my email address be better?
A Contact form is an excellent idea and pretty much mandatory for any online Business.
Cost you more in money? No, but if certain precautions are not taken you could lose your hair -- pulling it out in frustration.
Any form that provides for input of information and then eMailing can be used to send you Spam and/or send Spam to others. You should take the necessary steps in making sure your eMail address is not shown on the Web page and the form cannot be used by others for their own purposes.
Many free Form scripts are available or if not sure about how to do it yourself, purchase one that provides Support.
Not sure about pay-for scripts but here are two free ones.