'96 318ti, unknown service history

[firstbmw]

Hi everyone, great forum you guys have here. I have just bought my first BMW, a Santorin blue 96 318ti auto, Japanese import to New Zealand. It was running like a dog when I got it with a spark plug hole full of water. Cleaned that up and its running great now. I am going to try to get all maintenance up to date but my budget will stop me from doing everything at once.
First question. How do I check which engine I have? Registration says 1795cc, engine number unknown, and I can't see anything under the hood.
My rough plan is to do
oil and filter change,
coolant flush/replace, change out any plastic coolant system parts (can only see a small right angle elbow so far) ,
change auto trans fluid and diff oil,
plugs and leads.
In approximately that order. Have I missed anything more important than what I listed? Have I prioritized well?
TIA
John