A theory of simple classical fluids is presented in which both the static structure (on the "pair" level), and the thermodynamics, of all systems describable by spherically symmetric pair potentials, can be calculated by a unified approach. The theory is based on the diagramatic expansion of the pair distribution function that leads to a modified hypernetted chain (HNC) integral equation. It consists of the approximation that the bridge functions (i.e. the sum of all elementary graphs, assumed zero in the HNC approximation) constitute the same (universal) family of curves, irrespective of the assumed pair potential. Using the parametrized computer simulation data for hard spheres as input in the integral equation, it was found possible to virtually duplicate a large body of computer simulation data compiled for a variety of quite disparate interparticle potentials (the one and two component plasma in particular). The statement of universality enables to obtain the potential of mean force at small separations directly from the solutions of the integral equation, and the resulting enhancement factors for nuclear reaction rates (in the dense plasma) are in excellent agreement with Jancovici's recent calculations (by an indirect method) for equal charges, and Salpeter's ion-sphere prediction for mixtures