I have a city bike and it started doing some weird noises when brake.
I talked to my local bike shop and they said I should use some specific grease.
Unfortunately in the place where I am currently these brakes are not common at all and I will have to buy it in the Internet. I find several types though and I am not sure what I should use.
Which type of grease should I use for drum brakes?
Are you sure you have a drum brake? A "drum brake" is external to the rear hub and would normally be actuated by a hand-lever (rather than pedaling backwards).
Drum brakes (hand actuated types) themselves don't need grease. If there's contaminants on the drum or shoe, you should just get some "drum brake cleaner" from your auto supply shop. However, more than likely the 'noise' you're experience may be from the wear indicator on your drum brake, indicating you need a new brake shoe. Given that you don't know the manufacturer of your brake, this replacement may be hard to obtain but a new drum brake itself is cheap.
I wouldn't use any 'grease' on a hand-actuated drum brake unless I saw something from the manufacturer. Instead, for noise I'd first try drum brake cleaner from the auto-shop -- and if that doesn't work, maybe use some sandpaper on the drum shoes to deglaze them and take off any leading edges.
Related: When do I know the drum brake is at the end of life and needs replacement?
Single-speed coaster brakes are intended to be pretty much packed with grease. There is no part of a coaster brake that can be harmed by grease, so be generous in applying it. You should use a grease with tolerance for high temperatures, such as automotive brake grease, but even so, coaster brakes used in mountainous terrain can "cook" any common grease.
An internal-gear hub with a coaster brake may need more than one type of lubricant. Follow manufacturer's recommendations.
