Glasses in the BaO–SnO–P2O5–B2O3 system were prepared and evaluated in order to formulate preform glasses suitable for the fabrication of fiber cores with a very low photoelastic constant. A first glass system (I: xBaO–(60–x)SnO–40P2O5) was designed with a constant P2O5 content and various BaO contents (0–40 mol. %). Introduction of 3 mol. % of B2O3 to enhance the glass stability leads to the second glass system (II: x′BaO–(57–x′)SnO–40P2O5–3B2O3) with 33–38 mol. % BaO. The structure of both systems was investigated by 1D/2D magic-angle spinning nuclear magnetic resonance, Raman, and Fourier transform infrared spectroscopic techniques. 31P NMR showed the presence of Q2 and Q1 units in the first system and correlation 11B/31P NMR indicated that boron enters into the network as B(OP)4 structural units. The photoelastic constant was determined and the stability of the best formulations as well as their refractive index dispersion was established. The drawing temperature and isothermal heating time (without crystal precipitation) parameters were also accurately measured by using experimental time-temperature-transition. Considering that the refractive indices of the core and the cladding materials must match, detailed core and cladding compositions for a fiber enabling single-mode waveguide transmission were proposed.