I'll provide a rundown of the general organic chemistry textbooks I've studied in detail:
- Organic Chemistry, David R. Klein: A very solid introductory text. Emphasis is on expediency and development of intuition over rigorous theoretical correctness. The coverage of molecular orbital theory is extremely scant, and classic valence bond theory (with associated concept of orbital hybridization) is the major explanatory paradigm. This is probably the most accessible text for students with a minimal background, but it's also somewhat superficial.
- Organic Chemistry, Jonathan Clayden, et al.: This is a very thorough text, with a slightly wider array of reactions discussed than Klein's textbook (most notably in the coverage of organometallic reagents). Again, the MO treatment is lacking, but it's invoked more frequently than in Klein. This book tends to delve quite deeply into the mechanisms underlying specific reactions, making it rather lengthy. There's also some superficial discussion of HSAB theory, which is mostly (if not completely) absent in Klein's book.
- Advanced Organic Chemistry, Carey & Sundberg. This is something of a seminal classic, but it's not for the faint of heart or for those uninitiated in the fundamentals. Mechanisms are elucidated in great detail (primarily via MO theory, with results from both ab initio and semi-empirical methods), and the exposition of pericyclic reactions is notably excellent. It also contains a great deal of illuminating content on conformational analysis. This is definitely not appropriate for a first textbook, but I would consider it essential reading for advanced undergrads and above.
Ultimately, either of Klein's or Clayden's textbooks should satisfy all of your criteria, but I strongly recommend Carey & Sundberg for subsequent study, if possible.
Beyond those, I've found Fleming's Molecular Orbitals and Organic Chemical Reactions to be a very good introduction to qualitative MO theory, but it's not a general-purpose text. March's Advanced Organic Chemistry is the ultimate, all-encompassing reference manual, and I'd consider it the sine qua non of any good organic chemistry library. As an aside, McQuarrie and Atkins have both published very good physical chemistry textbooks, which in many ways have been more enlightening than any textbook specific to organic chemistry. I'm also a fan of Oxtoby's Principles of Modern Chemistry as a general chemistry textbook; its mathematical and physical rigor is incredibly admirable, even if it does sometimes lack severely in concision. I've also heard unanimous praise for Housecroft & Sharpe's Inorganic Chemistry, but I've yet to read more than a few sections of it.