The following reading list depends heavily on Ralph Cohen's advice. Much of the material is summarized in Ralph's lecture notes written with Voronov. In particular those notes have (I hear) a good bibliography.
We will begin with Sullivan and Chas's, definition of the String operations on the loop space:
Definitions of cyclic/hoschshild homology: For cyclic we have Connes' original paper, or the Loday-Quillen
paper, which gives a modern approach.
General relation of Hochshild and cyclic homology to the homology of loop
spaces: J. Jones' paper, "Cyclic homology and equivariant homology, Inventionnes, 87 (1987), 403-423.
Minimal models: D. Sullivan, "Infinitesimal computations in topology" Publ. IHES , 47 (1977) pp. 269–331
How the hochshild cohomology under cup product, coincides with the Chas-Sullivan product under the Jones
isomorphism: Ralph's paper with Jones, "A homotopy theoretic realization of string topology", Math. Ann. 324 (2002), 773-798.
Another approach which is simpler (although only works over the reals) using differential forms and Sullivan minimal models is due to S.A. Merkulov "A deRham model for string topology"