There is a free shuttle from and to airport at bus stop2, just outside the arrival hall but you will have to call them to pick you up.
I loved my room at Alex, I don't think they are all like that but mine (suite 1) was big, clean, comfortable, with a huge TV, sofa, minibar and a super Jacuzzi on the bathroom.
The train station that leads to Amsterdam (just 2 stops away) is at a 15 minutes walk, it is ok if it is not raining. Very calm neighbourhood, you will find a bakery, supermarket and a few restaurants very close to the hotel. No breakfast included, just a coffee machine outside.
Staff was very nice.