I have taken seven Indo trips - 5 liveaboard and 2 resort based. I have dove the Lembeh/North Sulawesi area 3 times, Raja Ampat twice, and Komodo twice. If liveaboard prices are OK - I would recommend Komodo as your first destination. Denpassar (Bali airport) is an easy connect from the states (I use AA miles so fly on Cathay thru Hong Kong) - and is a decent airport. Manado (airport for Lembeh) is also decent, although less flight options (typically Silk Air through Singapore). Sorong (airport for Raja Ampat) is not so nice, and you are going to lose a couple more days making flight connections (one each way).
Diving - Lembeh is still my favorite for muck/critters, and has nice blue water diving North (Bangka) and on the Bunaken side (2 hour car trip). Lots of resorts here - can get the full experience shore diving and save a few scuba dollars. But Lembeh is starting to show some strain from all the people (locals and divers) - but still great diving.
Raja Ampat has gorgeous reefs, lots of fish, lots of drift diving. The mangrove diving in the passage or off Misool makes for some great wide angle opportunities that is very unique. The pier at Airborea (sp) island is awesome (giant clams, soft coral on the piers, lots of critters under the pier), and reefs at Kri are excellent. For big stuff - they have mantas, wobegong sharks, jacks and barracuda. Raja Ampat is great diving - but harder to get to and not as much muck variety as either Lembeh or Komodo.
Komodo has a great combination - gorgeous reefs, and really good muck. Both my trips to Komodo were on the Arenui (fabulous boat - highly recommended) - round trip from Bali so no puddle jumper flights required (which usually have severe weight restrictions - expect to pay for luggage if you have to fly local). Komodo has several muck sites - with unusual suspects being world class (frogfish, coleman shrimp, mimic octopus, cuttlefish, tiger shrimp, stargazers, sea moths, much more). Castle rock is a great blue water dive (white tips, jacks, turtles, great vis, drift dive) and cannibal rock and yellow wall (southern Komodo off Rinca) are two of the lushest reefs I have ever seen. And right around the corner is Manta alley - tons of Mantas and we also saw a Mola and swordfish there.
All three locations are excellent - and I would love to do the transition cruise from Komodo to Raja Ampat (up through the Spice Islands); have heard great things about that trip as well. But for a first trip with somewhat limited time - I think Komodo is your best bet. Bali is great topside, has a pretty good airport, and great variety of diving. And the Komodo dragons are very cool as well!! Check out my Flickr sight in signature block - lots of Indo pictures.