I know we’ve said this before, but this is backwards. When you’re creating a character, their background will determine what their trained in. In turn, their background and their training will help to define who they are as a person.
Police (in the US) all receive a variation of Judo/Jujitsu that was brought back from Japan after WWII. So, when you say, “I have a cop,” they’re all going to start from that same basic hand to hand style. If you say, “I have a Marine,” then they’ll have been put through MAP. If you say, “I have a Marine who became a cop after he mustered out,” then they’ll have been trained in both. And the styles they learned professionally will always be their primary toolkit for dealing with problems.
It’s not uncommon for people who’ve been trained in a practical form to go out and learn other other martial arts as they get older, but their choices will be influenced by what they’re looking for.
For example: my Karate Sensei in college was a member of the city’s police department. He had gotten to a point in his life where he was more interested in the underlying philosophy and ethics of martial arts, and that had drawn him to Karate. (I’m not sure why Karate specifically appealed to him, and never asked.)
When you’re putting together someone’s background, you’ve already started to define their hand to hand training. If your character’s only martial arts training is recreational, then it becomes a question of what they would have access to, and what they value. Someone who’s taking martial arts as an alternate physical fitness routine isn’t going to go into Krav Maga or Systema, while someone who’s looking for effective self-defense probably wouldn’t look at Tai Chi (even though Tai Chi does include effective combat forms).
The best advice I can say, for things like this is: get into your characters’ headspaces. And, go (window) shopping based on their values. Look at the available martial arts, as they’re presented in ads, or other venues, and pick what your character would, if given the choice. From this perspective, it’s fine for your characters to make a “blind buy” based on the information they have. Again, practical forms of Tai Chi exist, but it’s entirely reasonable for someone to miss that, think of Tai Chi as a different flavor of yoga, and ignore it, when they’re trying to decide on a martial art.
Incidentally, all of this also applies to things like picking personal weapons, vehicles, and even clothing choices.
If you’re creating a detective in the LAPD they’re not going to be carrying a Desert Eagle, no matter how cool you think the gun is. Departments have very specific lists of issued, and approved weapons. Even though it’s an effective tactical pistol, and good enough for the Feds, they won’t have a SIG P226. They’ll have the Baretta 92, one of the approved S&W M&P pistols, one of the approved Glocks, or one of a handful of other firearms. Those are their choices. It doesn’t matter how comfortable or accurate a Walther P99 is, they won’t get to carry it while on duty. You can find these lists online, through searching, just remember, those lists will vary by department, so if you’ve got Chicago PD, NYPD, or FBI, the lists will be different. And, again, your characters’ backgrounds will tell you what weapons they can choose for their job.
Sometimes how long they’ve been on the job will be indicated in their weapon choices. The Shield’s Vic Mackey comes to mind as an example of this; he carries a S&W 4506, which went out of production three years before the series started.
Also, worth pointing out that SWAT and Port Authority will often have different carry lists from patrol officers. Incidentally, as an illustration why specific research is a good idea, Chicago’s Aviation Police Officers (police at O’Hare and Midway) are not armed. (The CPD maintains a separate, smaller, armed, presence in the terminals.)
Hopefully this will give you some material to work with, though, I’ll admit, it may be a little off the topic you were originally looking for.