Most used tool laying wood flooring will be a chop saw,
a track saw and a good jigsaw are also pretty useful/indispensable (depending on your level of frustration at using the wrong tool for the job)
I’ve never felt the need for a table saw.
If you’re taking the skirting off (I recommend) to hide the edges then you could do the whole job with a jig saw and a hard-point.
cutting the mouldings not the flooring (multi tool or hard-point and a scrap of flooring as a spacer and some skill) will give you a much cleaner result going around doors etc.