Color laser printers, especially the big high end office printers, have the color capabilities you need for printing the company logo and the occasional Excel pie chart - but they are truly bad for printing photos.
But the good news is that almost any of the current generation of ink jet printers, even the cheap ones, are pretty good at printing photos - but only if you print in the printer's high quality setting on photo paper, if you use the cheap office paper you will get the same desaturated colors you got at the office.
Now, the colors in print will never be the same as on screen, especially the brightness (because the screen is a light source and he paper isn't) but you can get good results results, here are the options depending on how accurate you want the colors to be:
1. Just print in high quality on photo paper
If you like the way colors look an screen right out of camera and you never calibrated your screen than it's likely you won't notice the problem from uncalibrated printer (but it will never be the same as on screen).
This should be good enough for most people and will probably match the results you get when you get the photos printed in cheap labs.
2. Calibrate your monitor
If you're serious about getting the right colors you first need to make sure what you see on screen is really what's in the file, this will probably get you predictable results (that is, the difference between screen and printer will be predictable and you can learn to compensate).
There are several systems that will let you calibrate monitors, some are not very expensive.
This should be enough for most serious hobbyists and pros
3. Use name brand paper that has profiles available
The next step is to use good paper and get printer profiles for that paper you are using.
4. Calibrate your printer
The next step is to get a device that can calibrate both your screen and your specific printer with the specific printer you are using.
Those are definitely not cheap and this should be good enough for everyone.
5. Know when to stop
This rabbit hole goes very deep, if you want truly accurate color you might find yourself in a black shirt (to avoid reflection) in a room with gray walls and special balanced lights (to avoid color casts) manually adjusting color space conversions.
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