Trains - there's no station at the airport but Edinburgh is small for a capital city and the airport

Hi Everyone! After lots of planning and many emails between cheap weekly car rentals friends, a lot of great tips from all of you... our trip to St. Andrews, Scotland is almost organized. The only thing I need is the name of a reliable car service to pick us up at Edinburgh airport and take us to St. Andrews... I have looked into trains (there are none) and buses but we will be traveling from Canada overnight to Heathrow then another flight to Edinburgh so I think we will be too tired to bus our way to St. Andrews. So....if cheap weekly car rentals anyone has any information on a car service it would be greatly appreciated. Many thanks in advance. Ptm
The train station that serves St Andrews is Leuchars, and there is a bus from the airport to the train station, however adding the price of bus+train+taxi to yput hotel (4.50+12 cheap weekly car rentals aprox+14 aprox) it only worth the trouble if you are one or two passangers. Last time I went from SA to Edi's airport on April I paid 90 pounds using a local taxi company, when I came back on May I asked at a booth at Edi's airport for the price to take me to SA and they said 110 Pounds (!). It was not the same company but I find it too expensive and I took the train, we were only 2 people. Normally taxis doesn't charge per passengers but for trip. But I do normally the trip from SA to Edi using local companies, so I don't know the policy of Airport taxis. (If you decide to take the train it is better price to buy a return ticket, you don't have to give a specific time/date of return only specify if is same day return or not)
Trains - there's no station at the airport but Edinburgh is small for a capital city and the airport is less thn half an hour by bus from the city centre where you can get a direct bus to St Andrews or a train to Leuchars cheap weekly car rentals (followed by about 10 minutes in a taxi). Alternatively cheap weekly car rentals you can get a bus from the airport to Inverkeithing, which also has regular bus and train services. This option avoids the element of doubling back that you have to do if you go into the city centre first.