As I already commented, the low level names of all Kp-Font variants are documented in the manual. But I must admit, that this may be hard to understand.
So I thought, I should show some examples here. Regarding your question in comments see at the end.
\documentclass{article}
\usepackage[latin1]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[english]{babel}
\usepackage{lmodern} % "Latin Modern" as default font set
\newcommand*{\testfont}[2]{\textsf{#1 (\texttt{#2}):} {\fontfamily{#2}\selectfont
Best off (sic!) 1234567890 Questions}\par}
\setlength{\parindent}{0pt}
\begin{document}
\section*{Examples for low level names of Kp-Fonts}
\testfont{Roman}{jkp}
\testfont{Roman light}{jkpl}
\testfont{Roman, large smallcaps}{jkpk}
\testfont{Roman light, no f-ligatures}{jkplf}
\testfont{Roman, large smallcaps, old style numbers}{jkpkosn}
\testfont{Roman light, oldstyle}{jkplos}
\testfont{Roman, very oldstyle}{jkpvos}
\smallskip
\textsc{\fontfamily{jkp}\selectfont Usual SmallCaps vs.\\
\fontfamily{jkpk}\selectfont Large SmallCaps}
\bigskip
\testfont{Sans Serif}{jkpss}
\testfont{Sans Serif, large smallcaps}{jkpssk}
\testfont{Sans Serif, no f-ligatures}{jkpssf}
\testfont{Sans Serif, oldstyle}{jkpssos}
\testfont{Sans Serif, very oldstyle}{jkpssvos}
\smallskip
\textsc{\fontfamily{jkpss}\selectfont Usual SmallCaps vs.\\
\fontfamily{jkpssk}\selectfont Large SmallCaps}
\bigskip
\testfont{Teletype}{jkptt}
\testfont{Teletype, oldstyle numbers}{jkpttosn}
\testfont{Teletype, oldstyle}{jkpttos}
\testfont{Teletype, very oldstyle}{jkpttvos}
\end{document}

For your document you should define one or two commands depending on, what you like better. I will use here the basic Kp-Font roman, as seen above it is jkp:
A switch similar to \rmfamily or \bfseries: \newcommand{\kproman}{\fontfamily{jkp}\selectfont}, but then you have to set it in a group. Compare what I did in the example inside of \newcommand*{\testfont}.
Similar to \textrm or \textbf a grouping command: \newcommand{\textkproman}[1]{{\fontfamily{jkp}\selectfont#1}}, note the doubled braces for the grouping.
\kp@petitesmajuscules\kp@flig\kp@styleis a series of 3 LaTeX commands, which are replaced according to the package options you give. This is shown in jfbu’s answer. – Speravir Jan 21 '13 at 18:57