One thing you will notice is that you will recognise the above classical pieces. However, personal suggestion, if you are starting out with Classical, try a wider range. Don't limit yourself to only large classical pieces...try some more intimate chamber etc.. Also, many Classical pieces includes slow and fast movements...
Some other suggestions for Classical noobs:
1) Vivaldi - 4 Seasons Violin Concerto...
2) Rachmaninov or Rachmaninoff - Piano Concerto 2 and Piano Concerto 3
3) Brahms - Double (Violin and Cello) Concerto
4) Brahms - Violin Concerto
The above are the more tuneful style of Classical music...to get you started..
