After having picked up some basic ideas - from sources mentioned above or maybe even from Kenji Ueno's Introduction to Algebraic Geometry, which according to the introduction is aimed at "scientists", not just mathematicians, and thus has almost zero prerequisites - you should not be afraid to take the next step and study schemes.
For this I want to recommend warmly the 3 little, undergraduate readable, books by Kenji Ueno, Algebraic Geometry 1-3, which appeared in the AMS series "Translations of Mathematical Monographs" as nr. 185, 197 and 218. Each of these tomes has less than 200 pages - and the pages are small. Yet the author manages to cover all the basic topics of scheme theory, painlessly and in a very friendly style. To read the book you do not need to have studied Commutative Algebra before - instead you can have a copy of Matsumura ready while reading Ueno; for all the results he uses he gives precise references in H. Matsumura, Commutative Algebra, 2nd edition, Benjamin 1980.
It is no accident that the AMS decided to have this translated this from Japanese, I find the text an extraordinary combination of good content and friendliness
