Sorry, I have never seen an acceptable tile job with 'peel and stick'. First you have a joint on all four sides of every tile. Second the tile will go pretty fast down the middle of the room, but the trim in pieces will take longer to cut and lay than the field.
I recommend new sheet vinyl laid over the old. It will telegraph the lines in the present floor but it has heavy embossing to help conceal those imperfections. You can lay the whole sheet out and orient it with your room, put some weight on one half of the sheet to prevent moving around, fold the other half back over the weighted half and spread cement on the bare floor, slowly move the folded part back onto the cement while rubbing bubbles out of the contact area with a towell, cut off the large waste pieces, press the edges with a wood block, trim the rest of the waste off very carefully, repeat with the weighted half and be sure to put base shoe or metal trim (in doorways) around the perimeter to keep the vinyl from drying out and curling up. Believe me, it is much easier and it gives you a seamless floor.