  The $K2$ Mission has photometrically monitored thousands of stars at high
precision and cadence in a series of $\sim$80-day campaigns focused on sections
of the ecliptic plane. During its second campaign, $K2$ targeted over 1000
young stellar objects (YSOs) in the $\sim$1-3 Myr $\rho$ Ophiuchus and 5-10 Myr
Upper Scorpius regions. From this set, we have carefully vetted photometry from
{\em WISE} and {\em Spitzer} to identify those YSOs with infrared excess
indicative of primordial circumstellar disks. We present here the resulting
comprehensive sample of 288 young disk-bearing stars from B through M spectral
types and analysis of their associated $K2$ light curves. Using statistics of
periodicity and symmetry, we categorize each light curves into eight different
variability classes, notably including "dippers" (fading events), "bursters"
(brightening events), stochastic, and quasi-periodic types. Nearly all (96\%)
of disk-bearing YSOs are identified as variable at 30-minute cadence with the
sub-1\% precision of {\em K2}. Combining our variability classifications with
(circum)stellar properties, we find that the bursters, stochastic sources, and
the largest amplitude quasi-periodic stars have larger infrared colors, and
hence stronger circumstellar disks. They also tend to have larger H$\alpha$
equivalent widths, indicative of higher accretion rates. The dippers, on the
other hand, cluster toward moderate infrared colors and low H$\alpha$. Using
resolved disk observations, we further find that the latter favor high
inclinations, apart from a few notable exceptions with close to face-on disks.
These observations support the idea that YSO time domain properties are
dependent on several factors including accretion rate and view angle.
