What is the theoretical maximum data transfer rate of a pair of wires in a phone cable?
There's one beautiful, simple equation that has it all, called the  Shannon–Hartley theorem:

$$C = B \cdot log_{2}\Big(1+ \frac{S}{N}\Big)$$

It says that over a channel with a given quality, the capacity (bit rate) C is proportional to the channel's bandwith B. The quality of the channel (signal vs. noise) hides within \$log_{2}(1+S/N)\$, and the bit rate includes redundancy (error checksums and the like).

The best data rate can be achieved with a low-noise installation of a channel that offers a high bandwith.

Of the wiring systems in question, a simple two-wire phone line will have the lowest bandwith and the worst noise properties (crosstalk and interference from neighboring lines, ...), twisted pair wires increase the bandwith and are more immune to external noise with an increasing "CAT number" (6 being better than 5e, being better than 5, ...) and systems with optical fibers are even better.

A telephone connection has an audio bandwith limited to a few kHz. Old systems had filters and the wires were often not capable of much more than the filter-defined bandwith. Digital subscriber lines (DSL) take advantage of the fact that many phone lines, when not being filtered, can take more than the mediocre audio bandwith of telephones. Beyond approx. 200 bps, it depends on the installation of the last mile and in your house (and your provider's willingness to use it in the best way). Typically, fiber can handle a greater bandwith than copper, but good quality can be achieved with copper, too.

Note: Someone selling you "Fiber to the Home" over copper wires is just doing (un-? clever?) marketing. Claude Shannon was way cooler, he didn't even care about the type of channel (copper, fiber, radio waves, whatever), he just looked at the bandwidth and the quality (signal-to-noise ratio). You can join Shannon and, like him, enjoy the theory and also don't care about the material of your wires. When I took my communication theory class at college, my professor was actually very right when he pointed out the beauty of shannon's work and said that the equation mentioned above was the E&nbsp;=&nbsp;mc2 of the information technology age.