It takes a lot more than a drill press to install a Floyd Rose right. It takes a very accurate ruler (a tape measure will not do), and it takes skill and practice. If you are going to do it, get it done professionally, but I would suggest not doing it.
The idea behind the two point systems (such as a Floyd) is that they reduce the friction in the system. Reducing the friction means it will come to a more consistent "zero" point, so the tuning will be more stable. It works, too, but there are trade offs. There is less contact with the body, which means there is some lose of tone and sustain. If you are doing anything less than major dive-bombing with your trem, I would advise against it.
The Grover is going to be better than the stock trem on your Squire. Think about it, the Grover costs about a quarter to half of the cost of your guitar, it would be hard to match that quality with the stock part. If you want the best possible part, though, I think you can not beat the quality of Gotoh's 510 line. The 510FT-2 should be a drop in replacement for your Squire, and is readily available through Allparts. They have (I believe, I am not at the shop with the catalog) others which are also direct replacements, but I know the FT-2 would work, as long as the Squire does not use a different spacing than the Fenders.
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