  We initiate the study of several distinguished bases for the positive half of
a quantum supergroup $U_q$ associated to a general super Cartan datum
$(\mathrm{I}, (\cdot,\cdot))$ of basic type inside a quantum shuffle
superalgebra. The combinatorics of words for an arbitrary total ordering on
$\mathrm{I}$ is developed in connection with the root system associated to
$\mathrm{I}$. The monomial, Lyndon, and PBW bases of $U_q$ are constructed, and
moreover, a direct proof of the orthogonality of the PBW basis is provided
within the framework of quantum shuffles. Consequently, the canonical basis is
constructed for $U_q$ associated to the standard super Cartan datum of type
$\mathfrak{gl}(n|1)$, $\mathfrak{osp}(1|2n)$, or $\mathfrak{osp}(2|2n)$ or an
arbitrary non-super Cartan datum. In the non-super case, this refines Leclerc's
work and provides a new self-contained construction of canonical bases. The
canonical bases of $U_q$, of its polynomial modules, as well as of Kac modules
in the case of quantum $\mathfrak{gl}(2|1)$ are explicitly worked out.
