You just need a negative scanner. You can get flatbed scanners with a light in the lid that do a good job fairly inexpensively these days. I just got a Canon 8800f not long ago that's doing an excellent job with my old negatives. I paid about $150 new on Amazon, but I'm sure you could find it or something similar for less by looking around.
As for properly colored, the software that comes with the scanner does a pretty good job, I'm finding, and it can be tweaked by you if you like. There's also VueScan software, which works really well, and even allows you to make a DNG file if you like. Either way, once scanned, they can be brought into any photo editing program you have for tweaking to taste.
You'll want to make sure the scanner glass is nice and clean, and that the negatives don't have dust and stuff on them before scanning. Kimwipes are great because they don't leave any fibers. Modern scanners of this sort also have some ability to take out a lot of dust and scratches without totally messing up the photo, and I find that it works reasonably well, when needed.
I shot the photo below on 35mm color film in 1992 in Miami just after Hurricane Andrew ripped through, and scanned the negative just the other day with the Canon 8800f using no special settings at all. It came out of the scanner this way, and all I did was resize it for the web and sharpen a little:
I shot the next photo last week with my medium format Mamiya RB67 on Tmax 400 black and white film, developed the negative in my bathroom, then scanned it with the Canon 8800f.
One of the things I've found that I really like about the scanner software is that it identifies all the negatives placed in the holder, which is 10 or 12 35mm, or 3 or 4 medium format at a time, previews them, then you can choose which ones you want scanned just by checking the box next to each one, and let it rip. Then you can do other things while it works. When it's done, you've got all your scans done, named how you want, placed in the folder you want on your hard drive, etc. Not much fuss involved at all.