Servicing Question and Rough Idle When Cold Question

Hi,



So I recently purchased (~2 months ago) a 2010 BMW 335xi MT CPO. Has about ~97,000 km on it. I had it down to the shop recently to have it walnut blasted and to look at a rattle that got worse which resulted in me getting brand new turbo's next week.



I wanted to know what should I be looking to do next for maintenance? The main one that I am concerned about is the water pump. Should I have them replace at the same time as the turbo's? I would hate to be stranded.



Here are my records, not including hardware fixes:



Before I bought it:

30,000km - Sep 9, 2010 - Oil Change

47,900km - Feb 18, 2011 - Service Vehicle Check

47,900km - Feb 18, 2011 - New HPFP

61,000km - Aug 11, 2011 - Oil Change

69,600km - Dec 13, 2011 - Brake Fluid Change

69,600km - Dec 13, 2011 - AC Microfilter Service

69,600km - Dec 13, 2011 - Replace Battery



After I bought/getting the car ready for me to buy it:

96,000km - Aug 20, 2014 - Oil Change

96,000km - Aug 20, 2014 - Valve Cover

97,000km - Oct 10, 2014 - Walnut Blast



Next:

Waterpump and Thermostat

Spark plugs and coils - I plan to buy that amazing deal on Amazon and do-it-myself.

Brake fluid

AWD Transfer Case

Engine Drive Belts (V-belt and Serpentine)

Fuel Filter

Power Steering Fluid

Flush Coolant

Diff Fluid

Manual Gearbox Fluid



My next question is, I have a rough idle, that I just noticed now that it is getting cold out. I just notice it in the morning. It seems to jerk the car a bit while I drive for the first 5 minutes. Is this a leaky injector? Plugs and coils?



Appreciate it. I am pumped about having this car. So much fun.



Justin