I replaced the battery in my 35i last September. The original battery (which had BMW labels, so I'm assuming it was the one fitted at the factory) was a lead acid battery, and I replaced it with a Bosch lead acid (as specified on the Euro Car Parts website). I've had no problems, the new one has a 3 year guarantee (4 or 5 years are available for more money). I did register it using Carly, but I don't think it really needed doing as it was the same type and amp hrs.
I think if you do have Stop/Start you may need the AGM battery.
The original battery was a lot heavier than the new one, I suspect I will find out why in 3 years...
Cheers, Dave