I know that depending on the style and instructor things may differ but what could a beginner typically expect in their first or second week of training in Wing Chun?
You're right, it will depend on what you said.
I guess I can only say what I experienced in my first couple of weeks.
I won't describe the names of various moves as it may be confusing at this stage, but we did a lot of pad work, bare-knuckle (which took some getting used to) a few combos, a lot of physical training to work up a sweat and get the core temperature up. Wing Chun is typically close ranged, and I had to get used to bare knuckle drills zinging round my face and full speed.
It ain't flashy, extremely simple in its application. There will be certain techniques, combos that may take some time for the muscle memory to pick up, but overall I found that after an 18 month break from training that I slotted right back into it.
Classes will differ from lineage to lineage and I'd guess even from sifu to sifu within lineages. My sifu trains us very hard. So hard physical training, pressups, stomach crunch, footwork drills that make us want to hack up, followed by a variety of training from week to week. One thing is, it's never the same from one week to the next, which keeps it alive.
We also do the Sui Lim Tao, the first form of WC, only for a few minutes at the end of the class, but we do it nice and slowly and controlled.
Regardless, I hope you enjoy it and get it as much as I do. Good luck, let us know how it goes.
Hagakure.