With compression, there's a lot of great choices these days. MXR probably make the most versatile, easy to find and one box solution. It's small, neat and does a great job. It's got all the control one could want...the only problem is that it may be a little daunting for a compression-newbie. On stage, I don't want to get into knob twiddling. I like to set my pedals like presets and kick em in or out...hence more than one dirt pedal on my board. But for Compression, I really like the EBS Multicomp. It's really simple with just a level and gain knobs. It's a no brainer and does all I need in that context. BUT I do have GAS for a FEA Labs Dual band compressor / limiter. So my board might change soon.
For EQ, again there's lots of great choice. The Sansamp Bass DI has rightly won a lot of hearts over the years. It sounds great and does a lot. It's got a baked in tone which is either "you" or not. I like to use a MXR Bass Pre-amp. It's got a 3 band EQ with a mid frequency sweep. I like the input volume and output volume...a nice touch. It has a DI too, although I've never used it. Like most of the great MXR pedals, it's small, neat and beautifully made...and it ticks all of the boxes one could want.
Also look up the Joyo American Dream / Tech21 blonde pedal. It's a great EQ and dirt pedal. You really can't go wrong with that pedal. The Joyo clone is cheap as chips and leave you wondering why other pedals are so expensive. It doesn't have a DI though and that's a deal breaker for some.
In terms of octavers and filters...my preference is for MXR. They just play well together so well. There are others, but for me MXR is a brand I can rely on and I know it's gonna sound great.
Chorus...Hmm MXR, Tech 21 or a step sideways into the TC Electronics Corona Chorus is a great option for something with more sustain and a lot more subtle. The MXR has a great flanger too...if that's your vibe. Again, no wrong decisions here...just different flavors and needs.
Ambiance...there's a lot of stuff here. MXR Carbon delay is a legend. TC Electronics Hall of Fame is really well regarded. But my fav is the Zoom MS-70 CDR. It does a lot extremely well and combines a lot of my favorite ambiance models into a one box solution.
Dirt...ah...well...this is the most difficult to describe in words and anything you buy will not be your last purchase in the arena. So I'll cut to the chase and say what's been working for me. I love the Joyo American Dream, but recently I've been having fun with a Wampler Ecstacy overdrive (love it) as a pre-boost for my Fairfield Barbershop. Seriously, between these two..I think I'm sorted for dirt. The Barbershop is amazing at adding dirt but leaving your tone unaffected and still sounding like your bass. Even at it's wildest settings with a clean boost in front (Wampler) I can still hear my bass and it's playing dynamics.