Hmm. Well, I'm always reluctant to tell people, "You should buy this book." What constitutes a good textbook is an immensely personal thing, and frankly I think that most peoples' opinions related to what books are good (probably mine included) are heavily influenced by the experience they had in the class they used it. This is particularly the case when people think a book is bad. I wager most of the people who don't like McQuarrie and Simon - and there are lots of them - aren't judging the book so much as the professor who commanded they buy it. Of course, if you are taking a class in a subject, you don't really have a choice of what book to buy - you buy what the class uses - but if you are buying a book for your own use, then you have options, and I think it's always best in that case to get a copy of the book you're thinking of buying before you buy it. If you can't find a friend who has it, most University libraries can request a copy through interlibrary loan. Check it out for a month, read through some of it, see if it has what you want. Going by reviews and personal recommendations is helpful, but it's hard to know what reviews are biased by things not related to the text itself and even if you trust the person making the recommendation, they really don't know what exactly you're looking for.
Anyway, I've always liked McQaurrie and Simon, but there are plenty of people who hate it. But there are plenty of people who hate every physical chemistry textbook. It's math heavy, for one thing, and doesn't have the best figures in the world. What I like about it is that it starts with quantum first and builds thermodynamics and everything else off of that, which is in my opinion how physical chemistry should be taught. Atkins is probably a more approachable text, but the idea of teaching thermo first is somewhat antequated in my view. No matter what book you choose, physical chemistry isn't the easiest subject to teach yourself. It's all about concepts, difficult concepts, and for this kind of material I really think you need a capable instructor. Even then you probably won't truly understand it - I think it takes trying to teach it yourself before it really starts to make any kind of sense. That's the way it worked for me, anyway.
So all that said, though I think M&S is the superior text and it's what I would use were I teaching the subject, if you are buying a textbook to use on your own, without external instruction, Atkins may be the better choice.
As for Harris - my recommendation is only superficial. I don't have any experience using it in a class or teaching from it. Mostly it's just from page-flipping. It seems to be an excellent book geared toward chemical analysis and covers the topics you have mentioned in good detail. I have not done any problems in the book so cannot comment on them. But I can say that it goes over analytical techniques in good detail in addition to just giving conceptual information. There are also several chapters on statistical analysis as well as chapters on common laboratory techniques like mass spec, HPLC, and so forth - stuff that is rarely found in general chemistry texts anymore and even less frequently taught in general chemistry coursework.
[Will you pardon a three second rant? The fact that chemistry curricula at most US universities don't include an analytical course like this (mine didn't) is a shame and the lack of statistics requirement, even a small section in general chemistry class, is borderline criminal.]
Anyway, if all that sounds like I'm backing off because I don't want to be accused later on of leading you to buy something you ultimately think was a waste of money, well... you'd be right.
I guess what I'm saying is that while I know M&S is a good p-chem textbook, even if it would be a hard read for a beginner, and Harris seems like a good analytical textbook, your best bet is to try to get a copy of any book you are considering buy and take a look at it yourself. In the end only you will be able to decide whether it covers the topics you need in a way that agrees with your learning style. It's better to find that out before you lay down upwards of $50-100. The good news is, of course, that you can always turn around and re-sell it on Amazon if you have to.