There may be some differences of opinion on this (like everything else, right?) but IMHO everything in Bullseye builds on developing the correct slow fire technique - correct stance, breathing, sight picture, trigger technique, etc. There's obviously a lot involved, and I don't pretend to be an expert, just a long-time enthusiast - so here's a place where you can learn from the experts:
http://www.bullseyepistol.com/index.htm
With regard to getting the most from that Mark II - you absolutely should try as wide a variety of ammo as you can get your hands on (get your hands on easily, that is - there's no point in finding out that your pistol really likes a particular ammo if you can't get it when you need it). You should test from a secure rest and also test (if you can) at 25 yards - it will be easier to see differences. Five-shot groups are fine to start but you may need to go to larger groups to fine-tune the selection. A real purist would set up a number of targets, one for each ammo, then fire one shot from Brand A, one from Brand B on the second target, etc., then repeat the cycle a number of times (as opposed to firing all Brand A, then switching to Brand B, etc.). The testing is less biased that way. Also remember that the most accurate ammo in the world is no good for Bullseye if it won't function reliably in your particular pistol.
Unfortunately, you can't really zero the dot sight, or any sight, from a bench. The way you hold the gun when actually shooting, movement between when the sear releases and the round actually leaves the barrel, recoil, and any number of other factors pretty much dictate that you need to do your zeroing by shooting exactly how you will in competition. Most people I shoot with zero so they hold the dot in the center of the black, but there are a few who swear by zeroing to hold the bottom edge of the black (i.e., a 6-o'clock hold as with open Patridge sights). That leaves me shaking my head but I know some guys who turn in very good scores with it.
The best tip I can give you is to watch a relay or two, if possible, before you shoot one for the first time. That way you'll know what commands to expect, when you can handle your weapon and (more importantly) when you can't, and just generally become familiar with the whole process. Bullseye shooters are some of the most patient and forgiving folks around, but they'll appreciate it all the much more if you're not holding up the line any more than necessary.
Second best tip - to move from slow to sustained fire stages in your practice get some sort of timer that actually starts and stops the string timing for you. Don't just guess - you invariably get a "free" first shot in every string that way and it won't feel anything like competition. Instead of firing a full string every time, set your timer and just fire the first shot of the string to develop the ability to get that first shot off quickly and accurately when the buzzer sounds. If you start a string, especially rapid fire, feeling that you've "wasted" time getting that first shot away it will mess you up every time. Once you get comfortable with that first shot the rest will follow more easily.
Best of luck with your new hobby.
