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I was thinking a table saw would be the best single main tool, plus a jigsaw or multitool for cutting weird shapes. If buying several then a mitre saw for cross cuts plus table saw for rip cuts would probably be best, but trying to be as budget conscious as possible (hence doing it myself rather than must paying a professional).
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Most people are using a track saw instead of a table saw on site these days. I use a table saw for smaller trim work and it's useful but not in the top few tools for flooring.
Hopefully you are putting the floorboards down with the skirting off, in which case ripping the edge boards down with a jigsaw or track saw works well enough as the cut edge is not exposed.
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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.
Are you sure a table saw is the right tool? We used jigsaws, multi tools, track saw, and mitre saw but didn't ever need a table saw. If you do need a table saw then if it's just for one job I'd be tempted to take the materials to a manufacturing joiner and have them do the cutting. The one near us is £40 an hour.