I like 7th chords, aka jazzy chords!
Disclaimer: I don't really know proper music theory, so I'll explain in semitones (one step up/down in the piano roll). I might also explain things incorrectly, but it works for me.
7th minor example: A-C-E-G (0-3-7-10)
7th major example: C-E-G-B (0-4-7-11)
Usually, I'll also have a note playing one or two octaves below (-12 or -24).
Any note can be the starting point for this formula. Cmin7 would be C-D#-G-A# - just count the number of steps from C, and you'll see the numbers match the 7min formula (0-3-7-10).
You can also move individual notes up or down one octave, to make transitions smoother (shift+up/down): C-E-G-A, E-G-A-C and G-A-C-E are all Amin7.
To get more sophisticated, there are other chords that work, such as 0-2-4-7, 0-3-6-10, 0-4-7-10, etc. I'm sure these have proper names - sorry about all the numbers!
It's also possible to keep the chord but change the bass note. Try Cmaj7 with an A as the bass.
Pros and cons of my way of doing things
Nearly all of what I've done throughout the years is trying all kinds of combinations of these chords, or just random chords. I've found this way of working to be very useful in training my ears, developing a gut feeling for what works, and having fun.
On my own, I can get by with my lack of theoretical knowledge (thinking in semitones, only using sharps, not understanding notation well, being confused by roman numerals, etc). I'm able to make music that I like, and I have decent ears.
I might have gotten the same results faster and better if I had bothered learning more than music theory 101, but I've never had the patience. I've tried learning the piano, but I always get distracted making tunes in Live and entering notes manually like I've done for 10+ years now. In the end, it's all about having fun anyway.