If you want really expressive pads, which foster dynamics and also allow you to do things like finger drumming (I really recommend questforgroove.com if that sounds interesting to you), the best pad controllers are the ones in the Maschine line-up, by Native Instruments. I have an MK3 but the more basic versions are also apparently very good. The layout is much smaller (4x4) but the pads are massive and super sensitive, they are a joy to play.
A lot of people also use Launch pads by Novation, I don't know much about them, but they are quite popular and they are, I believe, on the cheaper side. https://novationmusic.com/en/launch
Rumour has it that a Push 3 is not too far away, so keep that in mind when considering the Push lineup from Ableton.
Quick addendum here: I've got a Push 1 that I cribbed for $150 on Ebay a few years ago (a steal at the time!) and absolutely loved my time with it/Ableton Live. When I switched my machines over to Linux though, Ableton didn't follow, so instead I picked up Bitwig and tried using that as a drop-in replacement.
Now, Bitwig is a pretty dang good DAW (I could write an entire essay's worth on why I love it), but what really knocked my socks off was DrivenByMoss' extentions[0]: this guy wrote an impressively expansive Bitwig plugin that lets you use the Push as something other than a generic MIDI controller. What's more is that I think I actually prefer the DrivenByMoss workflow to Ableton's. Partially because of Bitwig's modularity and partially because of the degree of control on display, you can do some outright stupid stuff with Bitwig+Push that isn't really possible on Live. It really is some of the most fun I've ever had making music.
[1] - http://synthstrom.com/
[2] - http://monome.org/
Actually, just the NORNS itself is going to get you booted up with some ridiculously fantastic music theory, especially if you're the kind that reads the source ..
By the way, I've been using Plinky, a Eurorack module, with touch buttons in a grid layout: https://plinkysynth.com/
https://www.kickstarter.com/projects/birdkids/offgrid-make-m...
However I also have one of these that is also amazing, just a bit fiddly to wire up to the iPad:
https://www.amazon.de/Keith-McMillen-Instruments-Multitouch-...
Of course, and Akai LPD8 is cheaper, but also needs fiddling - which is why the OffGrid is my current "pad of the day" choice.
Most fun with Animoog Z, Beatmaker, Loopy Pro and Endless ..