Agreed, I had that setup and never felt it was good for improv. My goto is my small 9U 84 hp modular because I have all the controls on the front panel. Not having to jump around to different tracks and pages to get something going is a big deal for me. I leave it pre-patched and I always start with a blank sequence in Metron.
A picture is forming, for me…
I find with my AR I can start from the init drum kit and go off in many directions, fairly quickly (sample-based chopped up d&b would be a stretch). So for me, that’s a great improv and sketching tool, as well as a performance and production tool. The combination of synthesis, pads + sequencer is very alive.
But, on the other side… I can see how with modular “leaving it patched” or “pre-configuring an OT” could equate to “practice”. It’s the “doing, before the doing”. Building up muscle memory, licks, tropes and expectations, which you can later improvise within.
I take a couple of pocket operators with me when I go to places ill be waiting around. Usually Tonic & Arcade.
Ipad with Korg Gadget is quick and easy.
All elektron boxes on their own with some headphones can be jamming quickly on. I usually have 1 box underneath the armchair…
I think a basic set up is drums, bass, lead and a pad. So you will need a drum machine or a groove box and then a mono synth and poly. If you dont want to spend a lot you could start with model:cycles for your drums and it is capable for a nice bass also, but I think a mono synth is better for bass. Model:cycles is really fun playing with it and I can spend hours and lost in time. Anyway with every modern synth if you like it you can have a lot of fun.
@Octagonist post almost made me buy a M:C immediately, then @Kegeratorz reminded me I already have a DN 
I’ve been having fun with OP-1 and MPC1000. That’s considered a small setup, no? Or MPC1000 and Ableton Live, that’s been kind of fun, sequencing Live with the mpc. I was going to get a Push 2 again but at this point it’s not needed. Too expensive for me anyway. As soon as I got one, they would announce a Push 3 in like February or something stupid like that.
Besides the modular case I mentioned above, I also own Elektrons (RYTM MKII and Cycles at the moment but I’ve owned others) and I agree they are great for programming and squeezing a lot from a single box. I just think that for pure improv, having all the controls, modulation, mixing, etc in sight and wiggle-able at all times is most important, and just more fun to me. But it’s great to see everyone’s perspectives. And when I see some of you Elektron ninjas flying around on an OT or whatever, its impressive!
I find that the elektrons are great for preparing ideas and then jamming live, but they’re not my favourite tools for pure improvisation.
For me the DT and DN are instant creative machines. The longest part about starting fresh projects is picking samples for the DT. After that, it’s just metronome, live record, and let’s go.
Having a beefy monosynth join the party makes it even more fun.
It’s entirely possible that I’ve just not learned them well enough yet. I still enjoy the process, and I often really like what I create, but it takes me a little longer. It’s actually nice to have some prepared stuff on the Digi Twins and then improvise with other gear over top / along side.
They are really versatile boxes, which may or may not be a good thing for everyone. You can go super deep with crafting lines using plocks and conditional trigs, or you can just record raw and use LFOs and ctrl+all to mangle and destroy as you go.
My biggest hurdle is always the dreaded stuck-in-a-loop problem, where once I get something down I re-record or change without copying and saving, and lose little magic moments. But as a hobbyist who just likes to have a few beers and entertain myself with the bleepy-bloops, I can live with it. 
“Small”
I suppose that’s up for interpretation but the OP also said 3/4 items. My 9U 84 case is smaller than that.
Get the push 2 so they will release 3. Then you can sell me the push 2 for $400!
The last Push 2 I bought a couple of years ago came with a couple of dead pads. I think I’m gonna steer clear of Push. What I really want is a Moog Subsequent 25 (that’s also small so it’s relevant here). Used to have a sub phatty. Loved it. Push 3 is gonna have to wait 
nice! I use a 4u and 7u Intellijel case with Doepfer 6u for my modular portable stuff. Works great and not hard to carry.
modular is the most fun to me and inspiring. For quick beats, I turn to my Roland TR8, Roland TB03, OP-1 , Octatrack and Analog 4 as I can hash a quick set in minutes on auto pilot. I am ok with Elektron workflow but if I do not use it for a while especially with OT then I need to read the manual and watch videos as so deep.
My approach to managing samples is having spotify playlists that I sample from…So everytime I hear something I like, I put it in a playlist (Drums/General/One Shots). Then when I feel like sampling I just look through those playlists…
I could never have neat folders with ready-to-use samples, even if I’d like to. But this is the closest I’ve gotten.
I fully agree with this.
At times where I want to sketch out songs or sets, I love my Elektrons.
And at times where I feel like pure 4 on the floor techno improv I grab my modular. (Since I’ve added a Steppy and a Rample in my 6U case that is).
As you mentioned a small set, I’d limit to two boxes. Basically every Drummachine will do (as long as you have conditional trigs onboard).
Considering improvisation: Maybe a Soma Lyra 8 could be something for you?
It’s like an instrument you play. No menu diving, the approach far less ‘technical’.
(Mine arrived last week. I am going to hook it up with my MD - exactly for improvisation fun).