I have 2 out of 3 of these.
Choose the Fit if you do a lot of city driving, parallel parking, or hauling bulky items and boxes.
Choose the Corolla/Civic if you do a lot of highway driving, or if you'd like to maybe pull a little 4x8 trailer someday.
The cost of ownership, safety, and reliability will be about the same for all 3 of these. The Fit is the outlier, excelling in urban navigation and parking, and having a different cargo format that allows for moving things like chairs or large TV boxes. The Fit is a less pleasant choice however, for long road trips because the small tires don't float over bumps as well and there's a bit more engine/road/wind noise. If choosing between Civic and Corolla, I lean toward the Corolla because its base model is cheaper and because it has higher ground clearance. The Civic gets much better reviews though, and even offers a manual in its premium trim.
All 3 of these cars will only be available with a CVT transmission, which means you should change the fluid every 30k miles and pray for the best. Hybrids, from everything I've read/seen, have much more robust transmission designs that should last a lot longer. Hybrids also seem to go easier on the engines, which can be expected to last ~250k miles. For these reasons alone, I would pick the Corolla hybrid, which costs LESS THAN an ICE-only Civic with a potentially problematic cones-and-belt CVT design. The only problem is that the Corolla hybrid was only introduced in 2020, so there are no older models out there in the $4-$6k price range. The previous-generation Prius is also worth a look, although it is much more expensive than the similar Corolla hybrid.