Which TOTO ...[numbers] do I need .?

Well, if you want the BASIC TOTO Drake with a GMAX for the cheapest. The model number is CST744S. For the Sanigloss (Better bowl rinse) is CST744SG. But if you have a round toilet, you can NOT get the CEFIONTECT model sadly. And if you need any parts, you can use the OFFICIAL TOTO Parts store, that is actually GENUINE parts used by TOTO in the factory. I recommend to try to avoid from buying Fluidmaster stuff for your TOTO. The TOTO/Korky parts give a much more reliable performance. Please feel free to ask me or any other members on here for help. Hopefully you will love your TOTO!

Figure about 35-40% off the list price is the street price, so don't freak out. The original Drake, for example (CST744S) can be had for $200-220 in white.

Take a look at Terry's prices and pictures from the link above, and see what you like the looks of. All of the Totos at the level of the Original Drake or above will flush fabulously. If you want a little more bowl wash, the Drake II (CST454CEFG) is excellent (around $340 in white) and looks a little more modern. In a one-piece, the Ultramax II is excellent (about $440).

We have two original Drakes, among others, and highly-recommend them to everyone. I think they are a Best Buy!!

My only concern about the GMAX Drakes are, we have 2, 2005 TOTO Drakes, and 1, 2004 TOTO Drake ADA Height Elongated. The only issue is, the bowl can become dirty in just 1 week! I mean you have to clean the toilet AT LEAST every week. I might look into possibly getting a Double Cyclone TOTO Drake II down the road. But the GMAX has a STRONG flush and NEVER leaves shredded paper. So overall, it's still good for accept that one issue

The CEFIONTECT option (well, it's standard on some models and not available on others) does help keep things cleaner. This glaze is super smooth...sort of like just after you wash and wax your car...stuff doesn't stick. It is affected by mineral deposts and it will be degraded if you use any abrasive cleaners, but if treated right, it should help for a very long time. I have it on mine, and my mother didn't want to spend the extra, and there IS a difference.