As you said above, nitrogen has 2 s orbitals and one p orbital. However, one would typically freeze the chemically inactive 1s orbital, leaving you 5 electrons in 4 orbitals per atom, or 10 electrons in 8 orbitals for N$_2$; this is denoted $(10e,8o)$.
Going beyond the minimal STO-3G basis, in addition to the occupied molecular orbitals (which are poorly described by STO-3G), you will have a large number of unoccupied molecular orbitals that are necessary to describe electron correlation.
Choosing the active space for complete-active space (CAS) self-consistent field (SCF) calculations is traditionally quite difficult, see e.g. Int. J. Quantum Chem. 111, 3329 (2011). The traditional CAS-SCF approach is equivalent to exact diagonalization of the real two-electron Hamiltonian in the space of electron configurations, i.e. the full configuration interaction (FCI) method. Since the challenge of the FCI solution scales exponentially, in practice the problem size is limited in practice to $\lesssim(20e,20o)$. Because of this limitation, it is not possible to include all valence orbitals in the CASSCF calculation already for diatomic molecules; however, the results one gets with various choices for the active orbitals may differ.
There are a number of alternative approaches to the FCI problem, such as the density matrix renormalization group (DMRG) method or various selected CI methods, which are able to push back the scaling wall and which have been found to be immensely useful for chemical applications. As a rule of thumb, these methods can handle strongly correlated electrons in three dimensions up to problem sizes of roughly (50e,50o). Future large-scale quantum computers are hailed as a panacea for chemistry, because they might be able to push back the problem size limit further to hundreds of electrons in hundreds of orbitals, at which point full valence orbital active spaces become feasible.
Because of the importance of the choice of the active orbitals in traditional CAS-SCF calculations, a multitude of ways in which to choose the active orbitals has been suggested. For general 3D molecular systems, a variety of strategies can be chosen. Using the canonical orbitals is not advised, because the unoccupied orbitals are not good estimates of excited states. Instead, common ways to pick the natural orbitals include employing natural orbitals from a lower level of theory; for instance, unrestricted Hartree-Fock natural orbitals (UNO) have been found to yield good orbitals for CAS calculations; MP2 and CISD are other commonly-used alternatives. Another established alternative are the so-called improved virtual orbitals, which are a way to improve the choice for the unoccupied orbitals to include in the active space. It is also possible to define the active space directly in terms of a reference set of gas-phase atomic orbitals, see J. Chem. Theory Comput. 2017, 13, 9, 4063–4078
In diatomic molecules like N$_2$, the choice can be done simply by symmetry: as the Hamiltonian does not depend on the angle measured around the bond, the orbitals are periodic with respect to this angle, $\exp(i m \phi)$ (see e.g. Int J. Quantum Chem. 119, e25968 (2019)), and the orbitals can be classified into $\sigma$ ($m=0$), $\pi$ ($m=\pm 1$), $\delta$ ($m=\pm 2$), $\varphi$ ($m=\pm 3$), etc orbitals. In N$_2$, the two s orbitals both yield a $\sigma$ orbital and the two p orbitals yield 2 $\pi$ and 2 $\sigma$ orbitals, yielding an active space of 2 $\pi$ and 4 $\sigma$ orbitals (a $\sigma$ orbital fits 2 electrons, while the $\pi$ and higher orbitals each fit 4 electrons).
However, the choice of the initial orbitals should matter less and less when the size of the active space is increased. If all the valence orbitals fit into the active space, the orbital optimization in CASSCF should converge quite rapidly even when begun from the canonical orbitals.