might start here..

Here is a link that might be useful: shell rimula

Yeah, this stuff is confusing.
Having the same questions about my Lastec ZTR. Just sent an e-mail to the manufacturer, hoping for clarity.
Every manufacturer should plainly publish the correct oil weights.

I have a Honda CRV. The engine oil weight is printed clearly on the filler cap. Don't need to even look in a book.

Quick google search has these oils for these MFgs

Land Pride ZT60 & ZT72 Accu-Z
http://www.landpride.com/ari/attach/lp/public/specs/357-103s.pdf
20W-50 engine oil

Scag
STT-BSD - Sabre Tooth Tiger - turbo diesel
http://www.scag.com/OpManuals/STT-BSD/2006STT-BSDOPMAN/2006STT-BSDOpMan03173.pdf
20W50 engine oil

Ariens
http://ariens.custhelp.com/app/answers/detail/a_id/401/~/zero-turn-mower-oil
20W-50 (or 15W-50 synthetic) engine oil

Dixon
http://www.dixon-ztr.com/service-and-support/faq/
15w-40 full synthetic motor oil

Woods
http://www.woodsequipment.com/uploadedFiles/Products/literature/Zero-Turn%20Mowers%20Full%20Line%20B06010.pdf
20W50

Ferris
http://www.ferrisindustries.com/frequently-asked-questions/Service/What%20oil%20do%20I%20use%20for%20my%20hydraulic%20system/
Mobil 1 15w50 synthetic

Just to add webe2152, I don't think any ZTR get hydraulic fluid in the drive system, only motor oils. Seems the "Hydro" term is somewhat misleading, marketing pizzazz. Nobody has a "28 Ton" ZTR. :)