Cross border finance is the part of expat life where quiet mistakes compound for years, so it rewards early attention. The foundation is tax residency: spend enough of the year in a country and you generally become taxable there, sometimes on worldwide income, while your home country may retain claims on income or assets located there. Treaties usually prevent double taxation, but only when you file correctly in both places, and several countries additionally require declaring foreign accounts and assets, with real penalties for silence.
On the banking side, expect a sequencing puzzle at arrival, since accounts require documents that require accounts, and keep accounts open in both countries, because credit history does not travel. For regular transfers, specialist remittance services beat bank default exchange rates consistently.
Three habits separate the organized from the stressed: track days spent in each country, keep every tax and income document from both systems, and buy an hour with a cross border tax adviser when you arrive and before any property purchase or repatriation.