what's the cheapest and comfy way of travelling from HKIA to Tsim Sha Tsui?

Buses are cheapest. There are a few different ones that will get you to Tsim Sha Tsui. The "A" buses are quicker and cost around HK$35-40. The "E" buses are cheaper at around HK$12-15, but will take longer. The time difference isn't much though depending on where in TST you need to get to.

By MTR, you'll need to get the Airport Express and then transfer to the main system either at Tsing Yi (you'll need to transfer again though at Lai King) or once you get into the city. It could potentially be quicker to stay on the Airport Express until the end of the line and then go back up to TST from there.

The fastest would likely be to get the Airport Express to Kowloon and then a taxi.

It honestly depends on where exactly you need to get to in TST. I always use a bus (I live in Jordan, next to TST) since there's no need to transfer and the travel time isn't hugely different from using the Airport Express once you take into account messing around transferring.