From Jakarta? Good luck acclimatizing to the temperature here, for me it took around two weeks. it gets cold near 'maba season'. if you want to shower in the morning, prepare hot water. or even better get a kosan that has warm water. I didn't shower in the morning for my first two weeks here when I was a freshman in SMA.
Going cheap? my friends usually go out and ngopi every night, DON'T GO! it's a huge money waste. For food, prasmanan's are cheap if you know the menu to buy, experiment yourself! for living space, my ibu kos always said to me that there's a lot of cheap kosan near the river, there's also many good cheap kosan that's not on a main road, try to look inside jalan tikus/gang. for books, you can find used ones in pasar wilis. for transport, my friends always tell me to bring my own motorcycle, they say it's cheaper but I don't know the truth about that. Public transport is kinda good, the angkots here are pretty frequent but not too crowded that they block the road. so far, I haven't had an angkot ngetem for more than 10 minutes.
Speaking about transport. the roads here are narrow and there's not enough road for everyone so there's usually traffic jams in the rush hour. it's not to the point that it's not moving, it's just VERY congested so plan your morning accordingly.
The locals here are very friendly and down to earth, especially the older generation. study some basic 'arekan' javanese words and some malang slang, it will make it easier to socialize, AVOID USING LO GUE, THEY WILL THINK YOU ARE SOK KEREN. The Javanese language has a different more polite vocabulary when talking to elders and respected people, talk to them using formal bahasa indonesia just to play safe. I find socializing easy because I'm a native east javanese myself.
feel free to ask more questions! I'll gladly help!