I'd like to help clear-up some misunderstanding about C5/6 trans lubricants.
c4c5 Specialist is spot-on when he says not to use GM "Synchromesh" lube in C5/C6 manual transmissions. While it is specified for various rear drive manual transmissions and some front drive transaxles, it's not suggested for use in the Warner or TREMEC T56.
To meet warranty requirements and for cost-effective use in cars which see easy or normal driving, any brand of ATF which meets the Dexron III specification will work. For maximum trans durability, I recommend ignoring GM's suggestion that manuals never need to have fluid changes and adopt a 3yr/36000 mile fluid change schedule.
If you want premium lubrication, improvement in shift feel and (in many cases) a slight decrease in shift effort and you are willing to pay more for the oil, then Red Line D4 ATF (which meets Dex III) is an excellent choice.
If you drive the car really hard on the street in hot weather, you do occasional track day road race events, or you drag race regularly. I suggest converting to Red Line MTL which is a low-viscosity, GL4 gear lubricant, rather than an ATF. In extreme duty, the transmission's durability and shiftability will improve over that lube'd with ATF.
If you race a lot or your C5/6 is race only, you need a unique racing lubricant Red Line makes called "Superlight Shockproof Gear Lubricant". It's probably the ultimate manual trans lube for a C5/C6 but it has a downside--cold shiftability is not as good as that of D4 ATF or MTL, however, the problem lasts only a very short time. As soon as the gearbox begins to warm, shiftability improves.
As for automatics in C5/6, for warranty requirements and cost effective service, you want to use the ATF (probably either Dex III or Dex IV) listed in your owners manual.
If you desire premium lubrication use Red Line D4 Synthetic ATF.
If you are drag racing or road racing an automatic car on a regular basis one of Red Line's racing ATFs will be a better choice.
As for changing the lube in a C5/6 automatic, the automatics used in those cars do not have a conventional "dip stick". The trans fluid level has to be checked with the car up on a lift and running, by removing the trans fill plug and visually checking the level in manner similar to how you check the fluid in a manual. See the FSM for details.
For maximum transmission durability, I would ignore GM's "marketing scam" of a lifetime ATF and go to the more common 3yr/36000 mile fluid/filter change schedule.