Short answer: As cheap as you can get it.
Long answer: We generally define a "budget" phone as sitting in the sub-$500 space, either as its RRP or after a period of time as an expected price point for actual consumers to buy at. Over time the cost of a "new" phone – especially for Android phones – tends to drop, so it's not unusual to see phones that were more in the mid-range $500-$1000 price space appear in the budget market.