What type of wire should I use for my phone system?
In the past people used quad wire, or POTS wire. This wire is not twisted, is susceptible to interference, and is not suitable for telephone systems with several lines. If you are updating an old system and you encounter this wire, your best option is to replace the old wire with some type of twisted pair wire, such as Cat 3 or Cat 5e, rather than expanding the system with the quad wire in place.
Most installers have been using Cat 3 for phones, but Cat 3 is getting harder to find, and the price difference between Cat 3 and Cat 5e has narrowed considerably to around five dollars per thousand feet. Cat 3 is still recommended for phones, but if there's any chance that your phone system may be used for data transmission in the future, an upgrade to Cat 5e would be well-advised.
Aside from future-proofing, there is another reason that some people use Cat 5e for phones: simplicity of installation. If you are wiring for a computer network at the same time that you are wiring for a telephone network and the job is very large, you may find it easier to contend with one type of cable rather than dozens of boxes of different kinds. There is truly nothing worse in an installation than pulling a long run, especially one that requires fishing through small conduits and around tight corners, only to find out that you pulled the wrong cable.
There are a few installers who use Cat 6 for telephone systems. Unless the phone network may be used as a computer network in the future, this is a strange choice. It is the equivalent of using a speed boat to cross a swimming pool or using a chainsaw to remove a small twig from a bush--it's very unecessary, very expensive, a big hassle for what you're trying to accomplish, but it will work.