Slitherlink is incredible, you learn to recognize more and more patterns. And when you have mastered one variant, you can try with honeycomb pattern instead of squares or other shapes to explore new patterns.
Light up/Akari I have never quite gotten. It's either too simple or too hard, after learning the common patterns. I often end up just trying to fill in something, and backtrack when it doesn't work. Not as satisfying as deducing it would have been.
Hitori is nice, albeit a bit easy after having found the patterns. But relaxing to just comb through a few puzzles.
Shikaku, I prefer Tentai Show which is similar but arbitrary rotatable shapes instead, a bit nicer patterns to learn.