I have 3 completed projects using Nextion displays. I think they will do all you ask. I have not used any libraries, I had no trouble driving them with my own code. I will just point out that while I am very familiar with driving them with a PIC I am still finding my way around driving them with an Arduino. That said, it seems easy enough.Some useful advice here
Those look like a viable option and reasonable priced as well. 8 GPIO are plenty for what I have in mind. I don't know how the LED strips would like the 3.3v for the data. I'm going to be using either 2811 or 2812, haven't decided yet. A couple of the runs are a little bit longer, but I don't know how much that really matters in the end.
Are you aware of Nextion web site ?