Agent fees are normally paid by the landlord, so using an estate agent is usually free for the tenant.
Hungarian portals ingatlan.com and alberlet.hu carry the bulk of long-term listings, with English-friendly mid-term furnished options on HousingAnywhere and Flatio.
Single European emergency number 112, free and available 24/7 (ambulance also reachable on 104)
EU/EEA visitors can use a valid EHIC for medically necessary public treatment on the same terms, and at the same cost, as residents

Watch out for

Address registration is a legal obligation with tight deadlines (permanent address within 3 working days; temporary stays over 3 months within 15 days) and needs the owner's consent, so confirm the landlord will allow it before signing.
Rental scams have risen: never transfer a deposit or money before signing a written contract, and beware 'time-pressure' tactics and fake agents demanding upfront payment.
Non-EU nomads cannot use the public NEAK system without Hungarian social insurance (TAJ) tied to legal work/study or paid contributions; uninsured patients otherwise pay out of pocket (or forgo care) except for emergencies, so private insurance is effectively required
EHIC covers only medically necessary public care, not private clinics or planned treatment

Cost of living

Budapest

€1,250–€1,800/mo