First the font issue.

Yes you will have this problem all the time, as the font isn't available on the computer that is viewing your webpage, so it drops back to something a bit basic that is thinks is close, a fall back plan. If you specially want to use the font, design the image in say photoshop using the font of your choice an then place the image there, everyone will then be able to see the image font as you want it to be.

With the hosting, it depends on your ISP and if they will give you the address needed by Godaddy to point to your website where it is hosted in the name servers of Godaddy.