primary or logical and /boot
For safety, your Linux /boot partition should be 16-32 MB, and it must be within the first 1023 cylinders or 8 GBytes of your hard drive. It does not matter whether /boot is a primary or logical partition.
You can get around the above restriction, but following the above rule will make life easier. The other Linux partitions you need to create do not care whether they are primary or logical partitions either.
You can subdivide a primary partition into many logical partitions. If you are running a dual-boot system with Linux and Windows, I believe the Windows operating system needs to be a primary partition. Other Windows partitions do not have to be a primary partition.