There is a island hopper flying between Guam and Honolulu 3 times per week (in each direction). This flight stops in the Marshall Islands and a few other places (Chuuk, Pohnpei etc). I went to Pohnpei last year on this flight and it is a rather straightforward flight, the airplane is actually a Boeing 737 (would have expected something smaller). Flight numbers UA154 and UA155 if my memory serves me right.
One very important thing to be aware of is that although you might not have any plans of leaving the airport at Guam, you need a visa/ESTA for the US! You also need to pick up your luggage and check it in again, which also means that you have to follow US regulations and treat the trip as if your final destination was the US.
When it comes to prices and flight times there really are no ways of getting around this.
As for booking the flights I did it through a travel agent since we took this flight as a part of an around the world trip. However, I would consider doing the same even if you are justing going to the Marshall Islands, simply because it is such a rare flight to book and having an experienced travel agent that can find the best combination with other flights and assist if anything goes wrong is very good to have. It is going to be a costly trip anyway, so spending that little extra is something I view as a good investment.
As to where to book the layover you are really limited by when the island hopper flights are going. Most likely you have to make this layover in Guam whether you want to or not. The airport is open 24/7, so you can sleep on the floor if you want or book a hotel in the city. Although the airport is open all the time the check-in counters are not, so make sure to check when you can drop off your luggage. We decided to do it before they closed in the evening, went down to the city (taxies are available, possible to walk around 4 km if you really want to save a few $) and came back close to midnight to sleep in the terminal.