Basically what you'll do is use some sort of color picker to identify
white in the footage then use the software to autocorrect to that point. You don't add red in post processing - that's done with a filter during shooting only. What you're doing is compensating for the loss of red in blue water as you go deeper.
Most of the better editors have that function. Some also have a manual dial or levels that you can adjust for each of the color channels or across all of them. I haven't kept up with the latest versions so there's probably some that do white balancing automatically also now - it's not only used underwater.
My personal preference is Sony's Vegas Movie Studio Platinum - it's under $100 on Amazon or via download from:
Home Studio Family Overview
Other's I've seen/used are Adobe's Premiere or Pinnacle's Studio. My buddy gets good results with Pinnacle Studio without much of a learning curve. I believe VSMP has more functionality but is harder to learn initially. There's also Premiere Elements which is a less featured version of Premiere wrapped around menus etc. Any of these should be under $100 - most also have a free download trial version on their websites to try b4 you buy. All have upgrade paths to "pro" versions if you need that later.
To capture from tape - assuming you have a camcorder with Firewire (Sony calls it iLink) all you'll need is a firewire port on the laptop. And a cable - although some Sony's may have included it since the camera end is proprietary. Get a 6pin as it allows the software to control the camera. Since it's tape, you'll be capturing at 1to1 so I suggest reviewing/logging the footage before you capture it for editing.
If your laptop doesn't have firewire there are external capture devices that capture video for transfer via USB. If you need one, Pinnacle sells the Dazzle line - the better ones are HD IIRC. And they bundle it with Studio. Something like this:
http://www.tigerdirect.com/applications/SearchTools/item-details.asp?EdpNo=4949219&CatId=1428 I've never used it but did have an SD Pinnacle capture card about 10 years ago - it worked.
I see decent ones around $100. Ensure that they're HD, some lower priced ones downgrade the video quality during transfer. I don't think those Firewire=>USB cables sold cheaply on Amazon work very well - you probably lose color depth or HD with them. What do you expect for under $20?
If you have a Mac, you've already got Firewire built-in.