What changes are you planning on making to the theme? If you're only planning on making some minor tweaks with some additional CSS, then I would stick to using Fiji and put your custom CSS in CSS Overrides - makes your life a lot easier down the line when it comes to upgrading.
Creating a custom theme is really for when you want to create a totally new theme from scratch including totally new page layouts. The reason you don't see any widgets is because page layouts are defined in the database, and there are no page layouts defined for your theme yet. If you do decide to go down this route, then you need to do an export of the Fiji theme layouts, and then import them into your new theme if you want to start with the same layouts as in Fiji.
The other thing to remember is that once you make a copy of the theme, you no longer get the benefits of any style fixes we make to the fiji theme. If your'e implementing a totally custom theme this is not a problem as you won't have inherited any style issues from our themes, but if you're just copying our themes and making minor tweaks to the styles, then you have inherited the bugs behind any style issues we fix in upcoming releases, but will not get those fixed.