There are pros and cons for both options, you do need to have a slight relationship. If you try to ask as soon as you meet them, they will refuse.
Pros are that the ones that are more willling and easier to answer are the friendly type of sims. So try to find them and ask. Also, you can find a house that has several sims living in it and ask each person. Not getting dirty and stinky from the trash cans.
Cons, it can take a long time, I spent a whole day at the home of three sims to get my questions asked as I had to build a relationship with each sim. So, if you have met them previoulsy it can make it easier. You can also get, due to the stupid relationship glitch, ones who will then pester you for dates all the time.
Trash, Pros are quicker for the most part, and getting nice items as rewards, duck, bubble bath, books and more. You don't have to worry about someone calling for date because you asked them questions. More expensive homes will give more expensive items to be found.
Cons are best done at night (loss of sleep) and you may get caught. Most don't care but it is still a hassle. The lloss of sleep which can affect your moods. (if you have SN that is easily cured with the rocking chair, good for fun, stress and sleep). Messy and stinky. You will bring home some trash that you, or someone in the family, will have to clean up and you will definitely need a shower, so I think there is a slight loss in mood due to that.
You could, I am sure, do the trash raiding in the daytime and it may be better, as the sims might be at work. For a cop, it leaves the nights or weekends to do the raiding.
Definitely type up as soon (on computer click on writing, then report on . . . as stated earlier) as you can, you will lose the info if you wait too long, that has happened to me. Not sure of how many days you can delay, but I wouldn't give it more than a couple.
Hope that helps, if you keep up the other areas, hard working, relationship with boss, coworkers and such, it doesn't matter if you don't do a lot of reports. I'm not saying to ignore them, it depends on how fast you want to climb up the levels, what your goal is. Also if you have the default lifespan or have extended it are also factors to be taken into account. Longer lifespan means you can take longer to work on levels, but at default you will need to advance faster, so reports could be important.