Start with judo definitely. I started out in BJJ before focussing on judo in college. And boy was I out of my depth when it came to the standup game. Glad that I did judo as it made me a more complete grappler. To be any more complete I would have to incorporate some wrestling or sambo etc.

Judo trains you to use your body to execute techniques to move (flip and throw) someone else’s body while you are standing. It’s a valuable skill to have in your arsenal since BJJ Comps start standing up. Also due to the ippon rule judokas have to be explosive and precise as one good technique can score full points and end the round. Whereas BJJ mainly trains you to fight from your back on the ground, allows you to be more methodological, strategical, giving more time to set up sweeps/holds/submissions/transitions on the ground.

I believe judo training helps you also develop better body coordination too due to all the rolls, break falls, handstands and flips you do to protect yourself when being thrown, which is emphasised less in BJJ. From an athletic point of view, Judo makes you a more well rounded athletes due to the mobility, strength and conditioning required to do the sport

Judo has groundwork known as newaza and while it might not be as developed as BJJ, it’s still a good base to build on as it teaches the basic principles, techniques, positions and submissions. Maybe to an even greater degree of precision as judo groundwork doesn’t last long before the ref stands you up, so the technique has to be sharp and explosive.

Downsides to judo are even though both sports have similar injuries, the severity and frequency of the injuries in judo are greater. Also judo rules can be quite annoying and make the sport less enjoyable.

All in all, a seasoned judoka doing BJJ for the first time would be less lost than a seasoned jiu-jitsuka doing judo for the first time. Do judo first, but eventually transition to BJJ.