I've been training different martial arts for little over a decade now, but of course YMMV.

So #1 is you like the gym and the vibe. That means you'll keep going back and stay with it.

Either BJJ or Kickboxing (or any striking art) will get you into a general sense of "in shape".

In my experience (and I have #s from chest heart rate monitors to back this up), kickboxing does a much better job getting you conditioned than BJJ does, and if you just want to look good, hitting the boxing bag will get you a nice v-shape upper body, especially if you throw some push ups in the mix while hitting the bag.

Neither alone will get you ripped or build strength the way a dedicated weight lifting program will, if you just want to be able to pick up heavy things, practice picking up heavy things. :-D

Also you won't lose fat unless you also cut calories, I've rolled with plenty of chunky peeps in BJJ. Your body will want to eat more right after an intense class, you'll need some discipline to tell it "no". If you can manage that then you'll also shed the pounds, but even if you are in the gym 2 hours a day 5 days a week, you won't automatically lose weight w/o self discipline in the kitchen (but you will be able to eat a lot more before you start gaining weight, so there is that).

For BJJ gyms, take some sample classes at different gyms, see what they are like. Some gyms are guys in their 30s and 40s who have left their egos behind, some gyms are very "go go go" and will run you ragged. No judgement either way, I've worked out at both styles of gym and both styles can be fun so long as safety is paramount.

Safety should be discussed. You should hear the instructors talk about it all the time.

At a good BJJ gym, more senior students will be asked to help out the junior students, and roll with them and show them how to do things safely. At more ego driven gyms people with black belts may not even talk to people who are just starting out. IMHO avoid those types of gyms at all cost.

Same goes for kickboxing. Sparing is an important part of learning, the only way to learn how to dodge punches is to have someone try to punch you in the head. But good gyms don't want people getting hurt, and they should be very aware of TBI and how to avoid it.

I actually trained for a couple years at a professional MMA gym, and despite being really high energy with lots of shouting and hard core warm ups, they were incredibly serious about avoiding injuries during training. The reason was simple: Injured fighters can't go in the ring, and thus don't get paid.

I've been injured 3 times during training over 10 years, which IMHO is pretty good given at one point I was training ~15 hours a week.

Tip: In a good gym, the highest risk of injury comes from training with new students who don't know how to control themselves yet. Someone in boxing class who doesn't know how to pull their punches, or who doesn't understand their reach and bops you in the face by accident.

The 2nd highest injury risk comes from yourself and not knowing your own limits.

When I was just starting out I had a senior student tell me I needed to stop because I was about to break my own arm if I didn't tap out.

That is what a good training partner at a good gym does.