from the airport to Split centre

The best (budget) option to reach Split centre from the airport is to use the local bus line number 37 that departs from Trogir and reaches the very Split centre.

You have to know just a few useful things:

• change just a small amount of foreign currency at the airport (exchange rates at the Croatian airports are less favorable compared to the exchange offices in the town) or use an ATM; you will need Croatian currency to pay for the bus tickets

• after you have done the formalities just walk roughly 100 to 200 meters outside the terminal to the road that connects Trogir to Split; there you will find a local bus station

• wait for the local bus number 37 that connects Trogir with Split town centre; here is their schedule: http://www.promet-split.hr/index.php?option=com_content&task=view&id=94&Itemid=187 ; as you can see, they operate thrice per hour during the working days, so this is the option for you; please, keep in mind that this is not a schedule from the airport, but from the nearby town of Trogir, so allow 5 to 10 minutes more until the bus arrives at your station

• the price per person is roughly 3 EUR, but please, keep in mind that the bus driver will accept only the Croatian currency

This is by far the cheapest and most comfortable option! Please, do not hesitate to use it because the taxis are asking exorbitant prices for this route. Also, keep in mind that you will definitely need a small bottle of water and something to cover your head because it is quite normal to expect the temperatures to be quite above the 30 C! I am telling you this because most of the buses on the route that I have mentioned, don't have air conditioning system.
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Not all cabbies are out there to skin you. Verify the price with driver beforehand. Good option is the airport shuttle - it takes you right to the center of Split.

IMO the above described option is for masochists; to describe it as the most comfortable one must be out of her mind, with the bottled water or without it..

What is the approx. fare for a taxi from the airport to the center of Split?

I drove with this guys in June: www.transfer-split.com
Very pleased!

Anyone used the company Pleso Transport? I'm due to arrive next week.

30 kn one-way seems reasonable
here is their timetable

Does anyone know are the Pleso coaches easy to find straight out of the airport. Dealing with panhandlers and taxi touts at airports can be quite tiresome I'd like to cut straight to the Pleso desk/coach and buy my ticket.

taxi fares from split airport to split are aproximetaly 35 euro per car.There are websites like http://hbtransfer.com/ where you can chek all taxi prices in croatia