The discovery and development of methods to cool, trap and manipulate atomic ensembles have generated a revolution in atomic physics, culminating in the ever expanding research field of ultra-cold matter through the realization of Bose-Einstein condensates (BECs). Since the first realization of BEC more than two decades ago, the majority of studies were concerned with systems displaying short-range contact interaction. Following pioneering experiments in ultra-cold KRb, systems involving ultra-cold mixtures have rose to considerable interest through their capability to form diatomic polar molecules. The long-range character of dipolar particle interactions enables the study of a whole new spectrum of quantum many-body phenomena by giving access to the strongly correlated regime. In this context, NaK is a splendid candidate to investigate dipolar effects due to its large electric dipole moment of $2.72 \, $Debye, its chemical stability and the large history of spectroscopic studies devoted to its ground and excited state manifolds. This thesis reports on the first ever realization of a dual-species degenerate mixture of $^{23}\mathrm{Na}$ and $^{39}\mathrm{K}$. The experimental apparatus combines two pre-cooled atomic sources into a UHV collection region, where a two-color magneto-optical trap is operated. After transferring both species into an optically plugged quadrupole trap, the $^{23}\mathrm{Na}$ ensemble is cooled by selectively removing the hottest atoms from the trap through microwave transitions, while $^{39}\mathrm{K}$ is sympathetically cooled through its thermal contact to $^{23}\mathrm{Na}$. Following the transfer into an optical dipole trap, the mixture operation suffers from strong losses as the atomic clouds approach the high-density regime. Interspecies interactions are identified as the system parameter that drives the loss mechanism. In order to realize a quantum degenerate mixture, the dual-species collisional properties are investigated both theoretically and experimentally. By preparing both optically trapped ensembles in the spin state $|f=1,m_{f}=-1\rangle$, atom loss spectroscopy is performed in a magnetic field range from $0$ to $1000 \, \mathrm{G}$. The observed features include several s-wave poles and a zero crossing of the interspecies scattering length as well as inelastic two-body contributions in the $\mathcal{M} = m_{\mathrm{Na}}+m_{\mathrm{K}} = -2$ submanifold. Different magnetic field regions are identified for the purposes of sympathetic cooling of $^{39}\mathrm{K}$ and achieving a quantum degenerate mixture. Forced evaporation creates two Bose-Einstein condensates simultaneously at a magnetic field that provides sizable intra- and interspecies scattering rates needed for fast thermalization. The impact of the differential gravitational sag on the miscibility criterion for the mixture is discussed. The experimental setup and measurements are complemented by theoretical calculations that form a feasibility study of molecular NaK. Starting from ultra-cold Feshbach molecules, the study demonstrates possible pathways for the creation of ultra-cold polar NaK molecules in their absolute electronic and rovibrational ground state. In particular, a multi-channel analysis of the electronic ground and K(4p)+Na(3s) excited state manifold of NaK is presented. It analyzes the spin character of both the Feshbach molecular state and the electronically excited intermediate states and discusses possible coherent two-photon transfer paths from Feshbach molecules to rovibronic ground state molecules. %The theoretical study is complemented by the demonstration of STIRAP transfer from the X1Σ+(v=0) state to the a3Σ+ manifold on a molecular beam experiment. The experimental results serve as a promising starting point for the magnetoassociation into quantum degenerate $^{23}\mathrm{Na}^{39}\mathrm{K}$ Feshbach molecules. The theoretical analysis assures qualitative understanding as well as quantitative statements for the feasibility of the subsequent ground state conversion. In combination, they fill a critical gap towards the creation of chemically stable ultra-cold molecular Bose-Einstein condensates of NaK.