Is it cheaper to purchase on a website in e.g USD or local currency? the websites i purchase from will show the price for SGD. Assuming normal bank debit/credit card is used, which is a cheaper option?

This feature is known as Dynamic Currency Conversion (DCC). Often it is better to pay in the base currency of the website you are buying for, because the rate the website gives is deliberately marked up and you will be charged cross border fees anyway. Before you buy, always compare the provided exchange rate with the exchange rate displayed on Google.

However there are some foreign websites where it is better to pay in SGD. For example, the Taobao app allows payment in SGD (with decent exchange rates) and processes the transaction locally.

You can avoid these fees by using multicurrency cards such as Revolut, YouTrip, and the various banks' multicurrency debit card offerings. Some require you to convert currency beforehand (banks) while others can do on the fly (YouTrip and Revolut).