I shoot IPSC shotgun and it is a great time. I also started in pistol but as I prefer long guns as a rule shotgun made sense.
See my thoughts below from my experiences to date:
Birdshot - Shot size? Payload? Velocity?
95% birdshot / Usually a stage with slugs (maybe 10 or 15) and sometimes a stage with Buckshot (maybe 10 or 15).
Shot Size - #7.5 is probably most common, #8 would work too (might yield a slight advantage on clays with more pellets and only a single pellet hole needed to score but that is speculative on my part as I haven't tried it).
Payload / velocity is a tricky one. 7/8 would be best for action shooting as it should have softer recoil (and I find it does) but with semis they seem to run better on heavier 1 1/8 loads and reliability wins every time so thats what I shoot. If I find some 7/8 that is as reliable though then I would switch. Side note, there is a velocity limit in the rule book (1300fps) and some 7/8 may put you over (food for thought although I have yet to see a chrono at a shotgun match - YMMV).
Choke - Interchangable or fixed? Most used choke constriction?
For chokes it depends on the stage. Changing chokes makes sense for extreme stages (really close clays for example would warrant a switch to a wide open choke or far targets with no shoots close would steer you towards something with a tighter restriction - you get the idea). I use Light Modified in one gun pretty much exclusively and Skeet 2 in the other pretty much exclusively (they are basically the same thing). See below for chart as to why and what works where.
Round count - How many shells are you carrying on your person?
Before we get into that let's talk about gear (not sure if you have that covered yet or not). Most people are using King or Magload gear. What seems to be most common is a 12 round loader for weak hand and 28 round loader for strong hand. I run this and it works well, I have never encountered a stage where this wasn't enough (and it should always be enough based on how stages should be designed).
For round count it depends. Is the stage Option 1 (loaded) or Option 3 (unloaded)? Obviously Option 3 will require you to carry more rounds. Beyond that it also comes down to how much extra weight you are happy to carry (shotgun ammo is heavy) vs how comfortable you are loading and not missing.
Example, you have a 20 round stage and its an Option 1 start (with lets say 8 in the gun) so you need minimum 12 rounds. If you are confident you wont miss or fumble a reload then carry 12 but personally I would carry at least 16 or more likely 20. That way if you drop all 4 rounds round on the ground while reloading and have to grab another set or knock some off your belt accidentally you should still be good.
Sighting System - Bead, Ghost ring, red dot?
Bead for Standard or dot for Modified / Open. Personal choice. Ghost rings would work too but I dont see it much (not sure if I have ever seen it) as I find it slower (YMMV) but do what works for you.
Bonus tip. Get a "Matchsaver" on your gun if you haven't already, you will thank me at some point.