Notice: I just provide purchase links to show what i personally used. There may be better or cheaper options.

The LEDs

In many ways good parts are the key for this build. You need good quality LED strips in order to make your build suitable for Video and Photography work. Don't even consider using the cheapest LED strips available its very likely that your Photos and Videos will not only end up with a green or magenta tint but also skin tones will render horrible. Also high quality LEDs tend to be much more effective, wich means that you get more light for the energy you are using up. Therefore getting more out of the batteries you are carrying around. Especially for this portable build this is nice to have.

When buying the LEDs you should search for terms like "CRI", "Ra 80+", "Ra 90+". Sometimes such LEDs can be hard to come by by a reasonable price. Also consider buying the LED strips directly from china to save some money. You really should not spend more then 30€ per 5 meter roll.Try looking at places like eBay, amazon or aliexpress. Reasonable prized ones can be found here.

The case

The case should of course be big enough to house all the components and small enough so it can be easily carried around. Another important thing to consider when it comes to enclosure is heat! You want to choose a case that is able to dissipate all the heat your LEDs are generating. So a metal enclosure would be great because it saves us an extra heat sink. The area on one of the sides of your compartment should be big enough to house all of the LEDs you want (obviously). I used this one, if you are not from Germany try to find something similar on Ebay.

The batteries

When buying 18650 Lithium-Ion-Batteries it is important to look for good building quality. Don't make the mistake to buy the cheapest options on eBay. Those Chinese no name batteries won't make you happy because most of them won't hardly come over 900mAh also they are claiming absurd capacities like 9Ah or similar - It's just a lie. You should get some decent branded 18650s instead. Just look for common manufacturers like Sony, Panasonic, Samsung or similar. Those batteries will at least have a data sheet and hold their specifications. I recommend these batteries.

The BMS

A Battery Management System can be extremely helpful to make your lithium-powered project safe. They are very cheap and can be ordered for different configurations (1 cell, 2cells etc.). A 4 cell one can be found here

The display

The display is very cheap and only costs about 4€. It's a dot matrix OLED one with integrated logic so that it can be driven by I2C. Its size is roughly 1" diagonally. Just search for the keywords "1" display", "oled", "i2c" etc. An example can be found here.

The rotary encoder

The rotary encoder really makes the feel of the user interface. Using a rotary encoder with an integrated click button feels very intuitive and looks professional. Also its just one hole in the enclosure. A cheap one can be found here.

The DC/DC converter

You will need a step down DC/DC converter that can handle 3 Amps (at least 1.5). We will get 16.8 Volts peak from the batteries. And need to drop it down to 12V for the LEDs. Also you need a second voltage regulator for 5V. A 12V one can be found here. An example for a 5V can be found here. Maybe you can also make it into a power bank if you add a USB plug with decent current capabilities.