I'm a mum of 2, and I took up judo last year. I've graded to my orange belt.
Like you, I fancied doing a martial art and wanted to get fit. I've done traditional jiu jitsu before, but I couldn't find a local club, so I tried a BJJ class and a judo class. Judo is throwing people to the floor and then holding them there. BJJ is the same, but specialises in the part where you're on the floor.
Both were good. The BJJ class was much more masculine in approach. They didn't have an option for training just once a week (had to be twice or more), and it was a bit 'Bro'-culture. There was a thread on here last week where the poster's husband refused to miss their son's birthday morning because he had to get to his martial art class. It felt like that. (But other gyms may vary...)
The other thing to say about BJJ is it is very close contact. You'll be on your back with your legs around the waist of someone you've only just met. But it's also great exercise.
As for judo, I'm really enjoying it. It is challenging for us older people. You get thrown onto the mat, and when you've had two kids and you're slightly overweight (like me), that in itself is an accomplishment! It definitely has a competition side to it, although as a senior it's not as expected that I'll enter as it would be if I were a junior. Again, excellent exercise, and my body feels like it's becoming more resilient.
I would suggest trying out a few local classes and seeing which you 'click' with. Finding one you feel comfortable with, and where you like the sensei, will be important.