Help please! Looking to uplight these shelves - lighting novice

Hey gaffer friends. I'm a total lighting novice so apologies if my query is really basic.

I have these shelves both sides of a chimney breast (only showing one as the other is inaccessible while I'm painting!) - I want to install strip LEDs on top of both shelves, and want them to be connected (ie two separate strips, I do not want any lights trailing from one shelf to the other) - so basically two circuits across four shelves.

I also would love to be able to control both these circuits with a remote controller - ideally just one remote for both sides of the chimney.

Is this all possible? I feel like it is, I just have no idea what kit I need / what anything is called / how to ensure I can wire it safely and trust the product. I'm a woman living alone and I refuse to hire help for this because it feels like it should be super simple!!

Thanks in advance, sorry for what a basic request this is

Oh do I need neon flex or will a diffuser over leds suffice??