Literature
Here are some relevant book chapters, articles, and links.
Hilbert schemes and Chow varieties
J. Kollár: Rational Curves of Algebraic Varieties, Springer 1996 (Chapter I)
D. Mumford: Lectures on curves on an algebraic surface, Princeton Univ. Press 1966.
R. Piene, M. Schlessinger: On the HIlbert scheme compactification of the space of twisted cubics. Amer. J. Math. 107:4 (1985), 761–774.
R. Piene: On the use of parameter and moduli spaces in curve counting.
Dawei Chen: Mori's program for the Kontsevich moduli space \overline{M_{0,0}}(P^3,3).
Y.-H. A. Lee: The Hilbert scheme of Curves in P^3. BA Thesis, Harvard 2000.
Algebraic spaces
M. Artin: Algebraic Spaces, Yale Univ. Press 1971
A. Knutson: Algebraic spaces, LNM Vol. 203, Springer 1071
Moduli spaces of curves
W. Fulton and R. Pandharipande: Notes on stable maps and quantum cohomology.
I. Coskun: Birational geometry of moduli spaces. Lecture notes, 2010
D. Edidin: Notes on the construction of the moduli space of curves. Recent Progress in Intersection Theory, Birkhauser 2000.
R. Pandharipande: Intersections of Q-divisors on Kontsevich's moduli space...
R. Vakil: The Moduli Space of Curves and Its Tautological Ring. Notices of the AMS 50(6), 647--658.
J. Kollar: Holomorphic and pseudo-holomorphic curves on rationally connected varieties.
Stacks
D. Edidin: What is... A Stack? Notices of the AMS 50(4), 458--459
B. Fantechi: Stacks for everybody. European Congress of Mathematics, Vol. I (Barcelona, 2000), 349--359, Progr. Math., 201, Birkh?user, Basel, 2001.
A guide to the literature on algebraic stacks
K. Behrend, B. Conrad, D. Edidin, W. Fulton, B. Fantechi, L. G?ttsche und A. Kresch: Algebraic stacks. In-progress book.