I am afraid this is rather off-topic, but...
First of all - the band was disbanded and reformed a few times in the past. The only constant member has been Robert Fripp. It's his band actually...or rather his musical alter-ego. The band played different music in different 'eras'. For the very beginning I would recommend the 'Red' album - the most representative for their early style. I love the whole album but the last track - 'Starless' is a masterpiece. Check it out!
As for the rest of their discography...Their music changed drastically in the early 80s. The so called "colour" albums (Discipline, Beat, Three of a Perfect Pair) are, hmm, controversial but also very interesting. They feature a lot of guitar synthesisers, odd meters and interlocking rhythms. Try 'Discipline'. And rather avoid 'Beat'.
Their later albums include even more electronics and continue to explore rhythmic and harmonical boundaries. Their latest record - 'The Power To Believe' is excellent. Also try 'The ConstruKction of Light' - the title track is simply amazing. You should also give a chance to 'Eye Wides Open' DVD - marvellous!
BTW - there are numerous compilation aimed at the beginner, i.e. - 'Cirkus -The Young Person's Guide to King Crimson Live' or 'The 21st Century Guide to King Crimson'. Check them out. If you're more into electronica, try Robert Fripp's solo albums (Soundscapes) or collaborations with Brian Eno. If you want something rally weird - try 'Projeckts'.
Hope this helps. And hello everybody!
