The universal core is: your passport, proof of legal stay such as a visa or residence permit, and proof of local address, which can be a rental contract, utility bill, or sometimes a letter from your employer or landlord. Many countries add a local tax number, which you may need to obtain first, and banks increasingly ask about your foreign tax residency for international reporting purposes, so bring your home tax ID as well.
Employees are often asked for a work contract or employer letter; students for enrollment proof. Minimum deposits range from nothing to substantial depending on the bank and account tier. For business accounts, expect much more: company registration documents, articles, proof of business address, and details on shareholders and the source of funds, with compliance review taking noticeably longer.
The classic newcomer trap is circular requirements, where the bank wants an address proof you can't get until you have an account.