I've done a fair bit of "restoration" on some rarer lp's that are not easily replaceable. The software packages are a good start, but if you want perfection, you have to go in and redraw the waveforms manually. So I can tell you one thing - if the lp is replaceable at reasonable cost with a mint copy, that's the way to go if you value your time.
Eliminating virtually all noise on a VG- lp can take me about 16 hours of work.
The software has basically two functions: 1. find the click and 2. repair the click
The reading backwards approach will help in automatically finding clicks with less false positives. But no software is foolproof in that regard, and in addition, they all miss a lot of smaller clicks. Many clicks are not as sudden a transient as you might think, because they are compound problems - not just one isolated spike. Also, as the source music frequency rises, and the click magnitude and duration decrease (like "surface noise") noise becomes much more difficult for software to differentiate from the music. So to really clean up a moderately noisy lp you have to sit there with headphones, listening, looking at the wave trying to find the clicks which your software misses - and this can be very time consuming. Many small clicks are maybe 1/8000th's of a second in duration. Finding those in a five second snippet of music is not as easy as one might assume.
As to the repair function - software has maybe 30% of a human's intelligence when it comes to figuring out what SHOULD be where the click was. To fix a noisy section, it has to either apply some form of smoothing to the click based on a user definable algorithm, or interpolate what exists on either side of the damaged area, or outright copy and paste in a different area of the waveform. A human can just draw in what looks and sounds right with a much better reult. But this is very time consuming. Another problem with automation is the "repair" of false positives (especially as Eldartford correctly surmised, with electronic effects), which can really detract from what you're trying to do.
So the bottom line is - if you want an "acceptable" MP3 quality result for convenience, than probably any of the popular programs you find on Google will be fine. But if you want it really, really right, the software is just the jumping off point. (And you're wife probably won't be jumping with you :)
If you want to try one for free to get your feet wet, a good start is WaveRepair, which was written specifically for vinyl lp repair, and is excellent for manually redrawing waves. It's not so great at detection unfortunately so it's a mixed bag. It has a 30-day free trial that you can download and be playing with in 10 minutes:
http://www.delback.co.uk/wavrep/
It's not a full function, consumer-level, sound editor though and isn't great for quick, automatic fixing. I've become attached to it though.
I've also been meaning to try out Audacity which is totally free shareware, but haven't yet:
http://audacity.sourceforge.net/
Hope this helps, Chip