Creating a Strip of Light Using LEDs
What you are looking for are flat, wide-angled SMD LEDs. It will be easier to diffuse the light that way and will allow you to place the diffuser closer to the LED. You need to make some sort of diffuser to have the look you are going for. This can be made out of plastics or silicon. Since I am guessing this will be a hobby project, you will probably want to use plastic. You need to have a matte finish on one side of the plastic to diffuse the light. Cutting a piece of acrylic or polycarbonate, then sanding one side should work.
I feel like that will give you a good start. There are many ways that you can diffuse the light, the best solution would be up to you though and your application.