Options for custom firmware.
1. CyanogenMod firmware (or CM for short)
CyanogenMod is pure Android without adding chips from the manufacturer, a huge team of people are working on creating the basis of these firmware. According to statistics all over the world, more than 4.8 million phones cost exactly CM firmware. CM firmware is usually focused on reliability and performance. You can read more
Here.
Video review.
2. Firmware based on stock.
The point of creating such firmware in increasing the performance of phones while retaining all the manufacturer's chips. And again, you get the opportunity to choose which software from the manufacturer to keep and which to remove. As a rule, only such firmware appears in the first months after the phone enters the market.
3. MIUI firmware.
MIUI is a highly modified android, sometimes reminiscent of iOS. Most of the MIUI firmware is based on CyanogenMod and is released almost immediately after the official release of it. The main task of MIUI is to simplify the management of the phone and at the same time add to the interface of beauty and the ability to change the appearance in the root. You can read more
Here. Video review. 4. Android Open Kang Project (or AOKP)
AOKP firmware is very similar to CM, however, it is considered that AOKP has more settings that change the phone's interface and some functionality. The AOKP development team is much smaller than the CM, but it often happens that a group of like-minded people gather to support the popular AOKP device with the AOKP firmware.
5. Android Open Source Project (or AOSP)
By and large, AOSP is a bare android. The way it is released by Google, most often in such firmware minimal interface changes. Often, the creators of the firmware indicate in the name of their firmware "based on AOSP", that is, at the heart of the firmware is a naked Android.