Also very important is not to use old tyres even if they look great. The rubber goes hard and less flexible and can break up or lose grip more easily than new tyres. I have actually felt the obvious difference in grip when changing from old tyres to new.
Ten years and they are in the bin.
Many years ago, while working in the motor trade, I was asked to make my way to the M40 services near Oxford, to collect a car which the owner refused to drive any further, as the car was "shaking so much it's like riding a broncho" (to quote the customer) I met the owner, gave him the spare car, checked over the car he had been driving & set off back to London along the M40....Bloody hell, this car was a brute... The vibrations were worse than anything I'd driven before (and as a mechanic I'd driven a fair few cars...)
A little playing around with the speed of the car revealed it was at its worse at about 45-55 MPH, although it was fairly bad throughout the speed range. Engine speed & gearing made no difference, so my thoughts were tending towards drastic wheel imbalance.......
As I took the left hand filter from the eastbound M40 to the clockwise M25 the off-side front tyre burst. Terrified doesn't come near it!.... I pulled the car onto the hard shoulder & after a few minutes "recovered my composure" (understatement of the week!) changed the wheel and carried on back to Barnet. I took the car to our tyre depot & ordered 4 Michelin 165/13s, balancing & tracking. The result was a completely new car-it went where you pointed it, stopped when you wanted it to and a pleasure to drive. The old tyres, Stomils (the car was a F.S.O., a Polish Fiat) had been on the car since it initial sale in the 1980s and upon examination the internal wall of the blown tyre had come away inside the tyre. An external check would not have revealed anything was amiss, though.
So, lesson learnt.... NEVER compromise on tyres! The incident reminded me of my training manager, back in the 1970s, when I was an apprentice, who one said: "put the wrong oil in the car, it stops. Put the wrong tyres on the car, it doesn't......"
Sorry to have gone on a bit, but you CAN'T risk a mistake with tyres!