Well, if you click on a link to e-mail someone, it isn't going to be possible for the OS to open your browser, open GMail, and put the address in the To: field of a message for you so my first bit of advice would be to just not do that.
To change the default e-mail client, you need to open Mail and change the setting in the General preferences. I would pick your browser as the default app to see if that will work to at least launch it when you do this.
Personally, I would just set up GMail in Mail or Thunderbird rather than using the web interface exclusively - the main reason would be that you will then have an offline back up of all your e-mails. Without it, you are relying on Google not losing your data for you and, as good as they are, it is still possible that one day they have a catastrophic failure that wipes out your account. Without an offline backup you would be utterly screwed.