Ah, an important detail came to my mind last night, but it was too late to write it down. You probably won't be able to find old KAT-TUN videos on sites like Youtube. Welcome to Jpop *sigh* At least that's starting to change now. You can now find things like Number-i's works or Akanishi Jin's solo works on Youtube. Even Starto has started to open up on YouTube now, but old music videos are still hard to find. KAT-TUN is a somewhat unique group, it does not have a main vocalist, but it has two lead vocals (Jin and Kame), a rapper, a beatboxer/vocalist and two vocals. You will understand better when you watch the videos. However, another thing that makes KAT-TUN different from other Johnnys groups is their heavy use of rock elements. If you don't like rock, I guess it's hard to enjoy their songs. But there are also pop-oriented songs.
I recommend you Chinese sites like Bilibili. It's like a Chinese version of YouTube. At least you can watch old music videos, at least partially, in good quality. I'll leave you a few sample links, you can look at other videos by searching there or clicking on the suggestions.
their pop songs
https://www.bilibili.com/video…8.recommend_more_video.-1
https://www.bilibili.com/video…88.recommend_more_video.5
Pop/Rock songs
https://www.bilibili.com/video/BV1Vt411M7W7/
https://www.bilibili.com/video…88.recommend_more_video.7
https://www.bilibili.com/video/BV1ME411W7My/?p=3
There is no music video for these songs, but I personally like them so much. So I tried to find it from concert videos.