1) Definitely one from an EU country. The ability to live and work anywhere in any EU territory may be the single best passport feature in the world. Also allows you to bypass the new fingerprinting and visa fees Americans must pay to visit EU! Spain gives visa free travel to 175 countries, and is currently ranked #2 passport in the world, and has some benefits in some South American countries so I'd pick that one.
2) One from Japan as it will allow generous visitation rights to most Asian countries, and the ability to live in Japan! Singapore would be similar. China if you are playing the long game and want to help out your decendants, as they are a rising power.
3) I wouldn't really need a third passport if I had those 2, but if given three, I would pick one up from Switzerland, just because it's one of the most difficult countries to obtain citizenship, is a neutral country, and would give great social benefits living there. Possibly UAE for a totally different lifestyle.
United Arab Emirates is currently ranked as the #1 best passport, has the highest number of visa free countries, and no income tax, so that's probably the best single passport to hold, particularly if you want to live there. I don't know the entitlements for UAE citizens, but I assume it is similar to Qatar, where you get income tax exemption, free utilities, subsidies for marrying and having a family, a large stipend, money for a house, superb social benefits, etc. Also my US passport is rather powerful, but if I didn't already have one, I wouldn't want one (encumbers you with global taxation on any income you make, lack of social services, etc.).
A good strategy is to collect passports from regional cooperative areas, such as European Union, Southern Common Market, Association of Southeast Asian Nations, perhaps even UK for Commonwealth access, now that it's no longer an EU country.