You really do not need to bother with filling hairline cracks unless there is some "chipout" or pieces of concrete which are missing here and there where it has broken off the edge of the crack. I had a few, and just filled them with Quickrete brand elastomeric crack filler (it's available at Lowe's, in the aisle where they sell all of the concrete-related stuff).
I also used that same material to fill all of my 1/8" saw cut control joints, prior to laying VCT. I stuffed 1/8" weatherstripping down into the saw cuts, about 3/4" from the surface.
To date, I have absolutely no "telegraphing" of the saw cuts visible in the tile surface.
To prep, all I did was to damp mop, and vacuum. You really don't need to fret too much over it. Just make sure everything is smooth and clean. The VCT adhesive (I used Henry 430, from Lowe's) sticks like crazy.
I would use a cleaner like Castrol Super Clean and a stiff bristle brush to address any oily spots. As long as they are good and dry, although still stained by oil, you should not have any adhesion problems.
There are some pics of laying VCT in the build thread at the link below (towards the end)