These are my personal favorites I use:
First of all DELAY. The Roland RE-201 is a great companion, especially to the Voyager as it gives a bit analog detune that gives life.
My favorite outboard to the Minimoog is Lexicon PCM80 REVERB that gives exactly the lush I’m heading for. Turning up the time/decay of Conert Hall 1 and I’m lost in space

A good COMPRESSOR brings any Minimoog to life. For most of the sound of the Minimoog I prefer a VCA-type compressor. The SSL channel compressor (XR618) is normally my to-go-Moog-compressor. It can be run pretty hard and brings the attack and vitality from of the Minimoog. The DBX160VU makes a great work as well as the price effective and underestimated DBX163X (especially to Moog basses).
An EQ is useful as complementary to a compressor. Again I found SSL works great with the thick Minimoog sound. But it must be used carefully.
An analog step sequencer is always fun to control the Minimoog. I have not tried more than the one I have, the Doepfer MAQ16/3 (Black Edition) and so far I’m happy with it.
I haven’t jumped on the MOOGFOOGERS train yet, but it’s just a matter of time/money/space. Top of my want-to-try is the Delay and the VX351 and see how it can be transformed to music - at the end of the road it’s about music.
I don’t have it (other than UAD plugin) but use it frequently at a friend’s studio: The CULTURE VULTURE - gives some nice distortion making any Moog happy.