In the long term fitting decent puncture-resistant tyres will save you huge amounts of hassle and expense. Cheap tyres tend not to save money, once you factor in the time spent, plans disrupted, and (possibly) getting someone to fix the puncture for you.
Examples of good tyres that will minimise the number of punctures you get include Schwalbe Marathon Plus, though there are other brands too. The disadvantage of well-protected tyres is that some may not be as satisfying to ride.
Interested in particular tyres and want to find out how well they will protect from punctures? try https://www.bicyclerollingresistance.com/
