As far as compressors go, it depends on what you would like to achieve tone-wise as well as how much control you would like to have. Also, you might like to read a bit about different topologies like VCA, FET, OTA, Optical, Tube, etc. (
Types of Compressors)
I have recently got into a compressor shopping spree and am loving pretty much all of them. For simplicity, you cannot beat an LA-2A type compressor like Effectrode PC-2A or Universal Audio's UAFX LA-2A. These are two of the optical compressors, former of which has a tube gain stage, and the latter is simply the Universal Audio plug-in put in a box pedal form. I am getting Effectrode tomorrow afternoon, but I heard it a few times and it is one of the best compressors I have ever heard. UAFX LA-2A sounds amazing as well. Both are very easy to use and highly recommended...
On the FET side, Origin Effects Cali76 Compact Bass and Empress Bass Compressor get a lot of love around here. I have the Cali76 and love it dearly. I use it at the beginning of my chain and given its inherent color it just enriches my tone. I have not had the chance to try the Empress, but that is next in line for me. Both of these have lots of controls on, so if you would like to have minute tweaks, both are great. An alternative to these from Universal Audio is their 1176, like their LA-2A, a plugin packed in a pedal box.
@scubaduba has found it not a perfect fit for bass, but there are others who love it.
On the VCA side, I recently bought Carl Martin's Honey-Comp, which is quite easy to use (with only Comp, Level and Dry) and very punchy (as attributed to the dbx 160 family of compressors). I have not had a chance to use it live but at home it sounded very good. In terms of its form factor, it is very pedalboard friendly, so highly recommended.
If you would like to go for the tube route, there is the Markbass Compressore which cannot be beaten for the price! It is a real tube compressor with all possible controls and it is one of sweetest of the bunch. However, it is huge and current draw makes it a bit difficult to power up with most power supplies (it comes with its own though).
Anyway, I would definitely check
Compressor Reviews and
https://www.compressorpedalreviews.com/ before making the move. Even though Cyrus of Ovnilab has stopped reviewing compressors for a while, both if these guys share amazing information and they have big ears for sure!!!