No rig at all. The sound I hear in my head is more related to the sounds I like on records. More often than not, I prefer the sound on records to the live sound even of bands that can afford every gear and mixer they want.
For me a kind of game changer were mic preamps with transformers like the GAP DLX or the Warm Audio stuff and 19" compressors like the WA76 from Warm Audio (would like to hear the LA2 and LA3 clones from Warm Audio and GAP).
Or quality DI boxes like the Neve RNDI (couldn't afford the Reddit and never heard it). And the Pultec clone from Warm Audio.
One of the best things that happened during the last years is that quality clones of top analog gear have become affordable (relative!) without many or without any compromises in quality of the components.
Ever wonder why - with the exception of miced amps - amp heads are rarely used in top studios? Almost always DI boxes and mic preamps (outboard or quality consoles) are used.
I'm not into overdrive/distortion etc. More Funk, R&B, Reggae, Dub, Jazz, Soul and Pop than Rock or Metal. Although my roots are post-punk.
But even metal guys hardly use the DIs of amp heads for recording purposes. They might use miced cabinets a lot of the times.
For me rigs are stage monitors under my command (not that of any sound guy).
At home I have a bass amp, but I use a chain of outboard gear (Warm Audio Tonebeast/Warm Audio WA76/Warm Audio EQP into my SPL Crimson and small Adam Nearfields in combination with a TecAmp Pleasure Board. Love the sound I get out of that chain.
Live I consider a quality compressor like the Cali76 more important than the Markbass amps and cabinets I use. I like the Sansamp stuff, If I want a bit of grid and dirt.