The toilets that plumbers recommend are Toto, American Standard, Kohler and Niagra Toilets.
The best flushing toilets are the TOTO MS604114CEFG#11 Ultramax Eco One-piece Toilet with Sanagloss, TOTO CST454CEFG#01 Drake II Toilet with elongated bowl, KOHLER 3810-0 Santa Rosa comfort Toilet, American Standard 2034.014 and the Niagara 77001WHCO1 Stealth 0.8 GPF Toilet.
The make and model of your toilet is usually located under the toilet tank lid.
To find the make and model of your toilet carefully remove the toilet tank lid and set it gently on the floor, with the bottom facing up.
Look closely on the bottom side of the toilet tank lid for the manufacturer name or a number on the bottom side of the water tank lid.
Sometimes you may need to lookup the numbers on google search to find the make and model of your toilet.
Some toilets it can be hard to find the make and model of the toilet.
But most times the make and model of the toilet will be under the toilet tank lid although I've seen some toilets have the make and model inside the tank itself on the back side.
But most toilets including my toilet I have now in my house has the make and model located under the toilet tank lid.
If you can't find the make and model of your toilet but need parts for the toilet then you can take a picture of the inside parts and the parts should be easily found in most plumbing stores.
Most toilet parts are interchangeable but some toilets have different handles, fill valves etc.