  We describe an apparatus where many species of ultracold atoms can be
simultaneously trapped and overlapped with many species of ions in a Paul trap.
Several design innovations are made to increase the versatility of the
apparatus while keeping the size and cost reasonable. We demonstrate the
operation of a 3-dimensional (3D) magneto-optical trap (MOT) of $^7$Li using a
single external cavity diode laser. The $^7$Li MOT is loaded from an atomic
beam, with atoms slowed using a Zeeman slower designed to work simultaneously
for Li and Sr. The operation of a 3D MOT of $^{133}$Cs, loaded from a 2D MOT,
is demonstrated and provisions for MOTs of Rb and K in the same vacuum manifold
exist. We demonstrate the trapping of $^7$Li$^+$ and $^{133}$Cs$^+$ at
different settings of the Paul trap and their detection using an integrated
time-of-flight mass spectrometer. We present results on low energy
neutral-neutral collisions ($^{133}$Cs-$^{133}$Cs, $^7$Li-$^7$Li and
$^{133}$Cs-$^7$Li collisions) and charge-neutral collisions
($^{133}$Cs$^+$-$^{133}$Cs and $^7$Li$^+$-$^7$Li collisions). We show evidence
of sympathetic cooling of $^7$Li$^+$ ($^{133}$Cs$^+$) due to collisions with
the ultracold $^7$Li ($^{133}$Cs).
