Buying used is a significantly better value until ~$2,000.
Formerly cutting edge high end gear is more fun and reliable.
Entry level consumer cameras depreciate the fastest and hardest. New, they are the worst value. After a couple years or longer, they can become good values.
Cameras under $100
Search every marketplace you can think of.
Win an auction on eBay.
DSLRs under $200
Entry level DSLRs made around 2012 are the best value cameras. That was the peak year for DSLR sales.
Now there is an abundance of them on the used market. They are easy to find as complete kits with a lens, battery, and memory card. Some will have a second telephoto kit zoom, which is good for kids sports and lazy wildlife photography.
Nikon D3200
My go to recommendation is the Nikon D3200. It can record 1080p30 video and sees a 10 megapixel increase over the D3100.
The kit lens was an 18-55mm, which is perfect for general photography. A 55-200mm lens can be found bundled, or purchased separately. It’s an inexpensive way to be able to try sports, action, or wildlife photography.
There is a good upgrade path and Nikon DX lenses are the best value right now.
Canon T3i (600D)
The Canon T3i is the comparable model to the D3200. The front facing flippy screen and ability to run Magic Lanter make it a better choice if you also want to shoot video.
More than a third of the EF-S lenses Canon made were versions of the 18-55mm. The lens selection is no where as good as Nikon.
Nikon F Full Frame DSLRs
My favorite DSLRs for photography.
“Flagship” professional cameras have aged significantly better than swaths of newer entry level bodies. They will have additional features, we likely be weather sealed, have superior specs, customization buttons, and accessories.
Canon Full Frame DSLRs
The most popular full frame DSLRs. I think several are excellent values, such as the 5DS, 5D mark II, and 5D mark III.