In reply to guam737pilot:
For the technical details of the Matterhorn, it is best to search for the many, many threads on this subject (just enter "Matterhorn" in the search box on the top right). The Italian arete (I have not done it, or only the very top part of it), is mostly a quite long semi-technical route, with numerous fixed ropes, can be very exposed. Do not dismiss the seriousness of descending the Hornli arete, it is never very hard but seldom easy and more or less continuously serious - you never stop semi-climbing and it is sometimes quite full on.
But the real problem is that you need to be familiar with Alpine circumstances and situation. I think you would be better doing a series of Alpine climbs rather than Rainier, at least one to get to high altitude, e.g. the Zermat Breithorn which takes you to 4165m, to get some aclimitisation. You will need it, as the Matterhorn is just short of 4500m, you will suffer greatly if you have not previously been to comparable height.
It would probably be best if you looked at an entire Alpine trip before deciding if you really want to do the Matterhorn, get the feel of some other peaks that may be less crowded and frenetic than the Matterhorn. You may find that you prefer to climb things less busy and more personal. I doubt you could do this in less than 2 weeks, probably best to allow 3 weeks if you are coming from as far away as Guam.
Clearly you will need to get partners/guides organised beforehand to get the most of this. It is probably best, if you are following the guided route, to use an English speaking guide (I assume English is your native language), there are several (almost all British), who post on here, perhaps you should contact one of them.