Transfer from airport in Buenos Aires

You can take the Manuel Tienda Leon shuttle from Ezeiza into the city; that will take you to their main offices in the Puerto Madero area from which they will take you on to your hotel. You will see their booth as you exit immigration; a lion's head is their logo. They also offer service by remis (private car), and of course there are taxis, but their shuttle will be the least expensive. Check their Web site: http://www.tiendaleon.com.ar/ for more information.
Especially if you speak limited Spanish, that company will be a good one, because their staff at the airport speak English, and you can describe exactly what you need and be understood.
Manuel Tienda León shuttle is the best option. However, the shuttle doesn't work between 1 am and 6 am. So, if you arrive within this period, you have to get a remis.
Depending on what time you arrive in Buenos Aires you may want to check with the hotel on their check in policy. Some do not allow early check ins. They will keep your luggage for you but after such a long trip you will probably want to rest. So, there is no need to rush to your hotel in a taxi or remis if you cannot use your room yet.