There's not a lot of scheduled service to Majuro .... i was just there yesterday.
To the best of my knowledge, there are only two ways to get there (other than chartering a plane) ... Air Micronesia (Continental Airlines) serves MAJ from Guam and from Honolulu 3 days a week... (leaves from Guam and HNL on Mon, Wed, Fri)
Aloha also serves Majuro from Hawaii.
From Bankok, I'd get to Guam, then take Continental to Majuro ... you get to stop in Chuuk, Pohnpei, Kosrae, Kwajelein, and Majuro ... leaves at 8:20 am, takes about 8 hours, including stops.... 90% of the time, the best views of the islands are from the right side of the plane.
(also talk to the pilots when you get onboard... if the weather's nice, we'll make a circle before we land ... fly over the popular wreck dives in Trukk lagoon and such... make sure we know what side of the plane you're on)