Lucyn,
A 1-piece valve tends to be reduced port product, since the trim needs to be installed through the end connection. Generally they are flange valves and a sleeve is threaded into the port to contain the seats/ball and presses up against an internal seal (some very cheap NPT valves are also 1-piece). These valves tend to be lower end valves, and their level of performance is reflected in the lower cost.
A 2-piece valve is typically used for flanged applications and will be availagle in both full and reduced port. For maintenance the entire valve is removed from the pipeline. The 2-piece design is generally preferred when looking for a flanged valve, as it does have one less leak path when compared to a 3-piece deign. Many chemical producers and refineries have standardized on 2-piece designs for all flanged valves.
A 3-piece valve excels in applications where the end caps are welded or threaded in to the pipeline. The centre section of the valve can be removed from the pipeline very easily and repaired as needed. As well, one of the other advantages is the ability to have different end cap configurations. For example, a 4" reduced port 300# flange could be used upstream and a 3" full port NPT end cap on the downstream. Thus eliminating the need for a pipe reducer and allowing for greater flexibility.
A well designed 3-piece valve can be just as effective as a 2-piece or 1-piece. Generally, the body leakage rate will be irrelevant when compared to the stem leakage rate. Focus on the application and end cap configuration. If it is a flanged valve, look for 2-piece valves, If it is threaded or welded ends, look for a 3-piece valve.
There is no general rule that says all 2-piece are better than 3-piece. It very much dependednt upon process needs and more importantly, the design of the valve. A well designed valve will not leak, a poorly designed product will leak regardless of the configuration.
As for API 607 certification. You will find that all three configurations can be found with a fire-safe rating, however it is much easier to find 2 and 3-piece products.