A parlour guitar is slightly smaller than a dreadnought (a standard-sized acoustic guitar). These guitars came into prominence in the late 19th century, and became a favourite instrument of blues musicians in the 1920s. As the name implies, the guitar is best suited for smaller, more intimate performance environments, and sounds best with strings that highlight its improved tonal responsiveness. Older parlour guitars need low-tension strings to prevent damage to the guitar.
D'Addario Phosphor Bronze Lights
If you're stringing your parlour with steel, it's not a good idea to use anything heavier than light-gauge strings; most parlour guitar necks aren't built to withstand the string tension of medium-gauge strings. D'Addario's Phosphor Bronze Lights (EJ16 Light 12-53) have good sustain and a warm, well-balanced tone that shows off a parlour guitar's capabilities nicely.
Martin Classical Bronze-Wound Ball End
The original parlour guitars were strung with gut, and the material that comes closest to that sound nowadays is nylon. But nylon strings are usually used with classical guitars, where the string ties onto the bridge; parlour guitars use bridge pins, and require a ball end. The answer is Martin Classical Bronze-Wound Ball-End strings. These are regular-tension strings, so they'll give you a bright and responsive sound without risking your guitar's neck.