You will probably not get most reliable AND cheapest at the same time What is your priority?
Yellow Fish do a fantastic service, it’s about €73 Euro return which isn’t the cheapest but worth it for the service
Funny Orange quote 54 euros return for up to four people booked online in advance.
You can do it by bus for just less than €8, but that can take 3 hours.
The average price for a one way private door to door transfer is between €30 and €35. Anything cheaper will probably be a shared service, anything around €10 or less a 'shuttle' which might be a large coach and not perhaps be door to door.
Do a bit of internetting. search 'Faro Airport Transfers' then visit some of the websites for prices.
Price of private transfers will vary depending on the number of people travelling.
We have used Yellow Fish several times and found them a good reliable company to deal with.
Sunshine transfers reasonable and reliable
Yellowfish €64.00 return to Old Town, used them 5 or 6 times this year.
We used Bravotur €60 for private service. Really friendly and reliable.
You don`t say for how many ... that will affect the individual price. For one or two people, a reliable shared shuttle will be cheapest .. such as provided by Travel Republic through besttransfers4u ... should be just over 10 euros each. So if you are three, or more, one of the private transfers is better .