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For a first trip, that's perfectly fine. A lot of people will claim Vilamoura is too touristy, yadayadayadayada. Well, that has its advantages.
Here is some basic info,
http://www.vilamourauncovered.com/about-vilamoura/useful-information.aspx
You can get a bus from Faro to Vilamoura, which is cheaper, or get a taxi which apparently should be around 10€. Not sure about Uber but I think it's available too (it in Lisbon, although they sometimes have trouble with taxis). Have Uber installed just in case.
There is an app called MEO Taxi, never used and it does NOT appear to support Algarve. But it does Lisbon.
https://play.google.com/store/apps/details?id=com.geolink.android.meotaxi
This app does support both Faro and Lisbon but seems a bit crappy.
https://play.google.com/store/apps/details?id=com.interfacom.taxiclick
For public transports in Lisbon you can use Moovit.
https://play.google.com/store/apps/details?id=com.tranzmate
You can also simply use Google Maps for trains. I don't think it supports buses. To buy train tickets online you can use,
There are a couple of apps for pharmacies too, although Google Maps should have you covered. Anyway,
https://play.google.com/store/apps/details?id=com.milempresas.farmacias
Of course it may be simpler to just ask people. They will be happy to help. Buy it doesn't hurt to have a few apps in the phone.
Finally if you do stay in Vilamoura, you may like this little restaurant called "A Taberna", around the Marina area, as it is relatively cheap and very traditional (unlike most others in the area which either send foreign food, of Portuguese but very expensive).