Recommendations

Have a look in the Naxos section, they have some good starter compilations. I was a bit like yourself, but I bought a great Naxos album a few years ago called "Discover Classical Music". It was a double CD of music starting with Gregorian chants and progressing in a roughly chronological order up to early 20th centiry composers like Gershwin. Also included were two booklets, one about the music on the CDs and the composers, the other on how to compile a classical collection with suggestions of works by dozens of composers. I've no idea if it's still available, but it might be worth hunting down as it gives you a good idea of many composers work and has extracts from a lot of well known pieces.

As for specific stuff, you can't go wrong with a bit of Beethoven. Check out his 9th Symphony ("Choral" - Ode to Joy, the EU anthem) for something stirring, or Moonlight Sonata for something moving.

HMV's own Classics label have Moonlight Sonata on a CD with 3 other sonatas, but it's titled Moonlight Soanata. You should be able to find it in one of their stores easy enough.