I've just returned from this trip and had a wonderful time. The internal flights are with LAN Airlines. It's a good airline, nice planes, lots of leg room and the flight attendants were friendly - I think it's a much nicer airline than Iberia. The coach journey from Cusco to Puno is very long (about 7 hours) but they make quite a few stops at interesting places so the time goes quickly.
When you do the Amazon add-on, make sure you take plenty of insect repellant, wear long sleeves and take lightweight rainwear - it can get very hot and humid even though it's raining. The lodges you stay in are very basic but they are set in very beautiful surroundings. The food is great - plain but plenty of it.
If you need any further info, just let me know.