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When you book your taxi with https://booking.com the price is € 22.14 When you take Malta transport the price is € 2.20 . Take bus X5 to Marsaskala and from there take bus 124 to Birgu.
While the suggested bus route is cheapest by far, it may not be very convenient especially when travelling with luggage. You do however have the white-taxi service available. There's a kiosk at the corner to the left as you exit the customs control inside the terminal. They should have a fixed pricelist to all locations so you can enquire there before heading for the bus terminus. Another option and certainly cheaper than these is the Easy Cab service but you would have to pre book by appointment. You can get a quote for their service here: https://www.welcomepickups.com/malta/airport-transfer-book/
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