Shady is right, and you have received false information. The driver cone and dome materials make for little. That is in the balance of the speaker and a function of the designer.
None of us have heard many speakers, and practically never done serious listening. to many speakers other than what we have owned.
So we can't help you. You can start be looking at measurements. However, a speaker can measure well and still be a dog. However if it measures badly, it will be a dog. So you can exclude speakers that measure badly, but after that you are on your own.
I consider myself lucky, that I have never had to speaker shop, as I am the designer and builder, and I thank my lucky stars for that every day.
Some of the information you quote here is in the laugh out loud category.
For example, a speaker with a 3/4" dome may be a very good speaker. In general a 3/4" dome will perform better than a 1" dome. However there is a catch, as a tweeter needs to be shut down by the crossover so that it is down an octave preferably, at the speaker resonance Fs. That generally means a tweeter that is 3/4" needs to be crossed no lower than the 3.5 to 4K range. That means it needs to be used in a three way design. Further the mid will have to be a good one, and cover the speech discrimination band. So a good mid needs a bandwidth of 400 Hz to 4 KHz preferably. Unfortunately there are few that can do this at power, and I regret to say there are fewer now than there used to be. That is an indictment of the speaker industry. The reason being that, the speech discrimination band is where the ear is most sensitive.
There is a lot of work that has to go into a good speaker and that is the reason there a more bad than good, but I think the tide continues to turn in the right direction.