The menonite builders (there are several companies)Â certainly make good houses. Problem is they have become more popular of recent years and there can be quite a wait.
It is usually a good idea to have the house put up on concrete posts, which is a seperate build not done by them, and would have to be in place before delivery of the house.
My houses were both built by local builders I have 2 x2 storey houses. the first was on 9 foot concrete posts, went up from foundations to living in in three months, still at that time needed a lot of internal finishes but the essentials of rooms plumbing and electricity enabled my son to move in. ( we have Solar electricity) We built the lower floor under with concrete walls at a later date. A good solution as initially we did not know how much room we would need.
The second was designed as concrete ground floor and a wooden second floor with large wrap around decks from the start. That house took a lot longer being both bigger and fully finished, in all about 10 months start to finish but there was a months hold up 3/4 the way through due to Hurricane Earl.
 The Builders I used were fairly local to my property and both small family businesses, I saw previous examples of their work prior to choosing them. The only reason We used a second builder for number two house was the first business admitted he is mainly a shell builder and doesn't really do the finishings, like cabinetry and decor, to the expertise I was likely to require.  During both builds I never lost any materials from the site and both kept meticulous records for all costings.
So if you want to build My advice is try to find a local Belize family business, and see finished builds they have done, they know all the problems Belize can throw at your house and they have their good name to protect.
Some Bigger building companies while having all the qualifications and boasting Expat ownership, are usually able to produce a very good houses, but they still employ local workers who may or may not be good at the job. and the costs are often much higher.
I have heard complaints that one 'named' builder/contractor employed rarely turned up on site and did not check enough on Quality of workmanship, allowing dry wall to go up without a layer of tar paper( probably not its real name) on the exterior walls, which caused major water damage in the first real storm of the rainy season.
I am based in the middle of the country so only know my own area.