Hello there, just to share with you on my past experiences on my batam trips. Im not a guru, just my 2 cents.
To start off, just bring along your passport on yourself at all times.
There is soo much that batam can offer in terms of vice but its mostly vanilla services. So 2d1n is actually pretty ideal, im actually going over on coming 12, 13 October too.
With regards to a place to sleep, I dont think it matters much if you're intending to go to hallo kitty/octopuss as your deed will be dome there and then. HK does have outcall but its by another agent who in a way collab with them, the price point is on the higher end, so if you wanna get overnight bookings, there are plenty of cheaper options around.
The best thing about is their spas which provides double hj, this is the best of value in terms of looks/ money spent in across SEA. There are plenty of such spas mentioned in this thread, so pick your poison.
Hope you have an enjoyable trip, cheers.