I just bought the Players Handbook paper copy but I'm not sure if I should highlight the pages.

I don't know what you mean by highlight pages. Do you mean marking them using a highlighter pen? I mean, you can. It's your book, do what you want.

If that's not what you mean, can you please clarify your question?

There's a million of them in circulation, it's not like you're ruining a collector's item. Unless maybe it's one of the variant covers. But I'm not sure the pages won't smudge your ink.

You can; I don't think you should. I use a bunch of post-it notes and tabs for easy reference, that does the trick for me. Highlighting has never really been useful to me though, I've always prefered annotating texts.

Shoot, when I still purchased hardcopy I would use highlighters, pencils, even write in the margined in ink. It’s the same way I used to markup my textbooks for school (when I didn’t have to turn them back in). I never used copybooks for taking notes, I wrote directly in my textbooks and only ever needed to study from the one source. And since the textbooks were worth less on trade-in at the end of the semester than the copybooks would have cost at the beginning of the semester, the way I looked at it I was saving money (and trees) that way.

But that’s me, I’m sure I’ve just appalled some people at the notion of permanently marking up a PHB (or textbook). What holds the value to you: the book or it’s contents? If it’s the contents then do what you want with your own property. If it’s the book, try (and I do mean try) to keep it pristine. (Be warned, sooner or later someone will accidentally knock over a cup of coffee or pick it up with greasy pizza fingers. We call that “patina.” 😉)

I find that highlighting my books doesn’t help but putting labeled tags on the pages so I could find the sections quickly is very helpful. Even the older books I’ve been repurchaseing I add tags to since they are all for reference. 

Quote from Wi1dBi11 >>

I find that highlighting my books doesn’t help but putting labeled tags on the pages so I could find the sections quickly is very helpful. Even the older books I’ve been repurchaseing I add tags to since they are all for reference. 

 
I also find highlighter to be less than helpful. I have used color coded tags, like my 2e MM. I often enough just dogear page corners though.

Ok, thank you for the advice everyone, thank you very much.

i'd say DON'T...use stickies like others are suggesting

Otherwise, you're going to highlight something now and in a month highlight something else, and something else in another month.  And then you're going to have a crapton of highlights that you no longer want.  It's not a one-time test you're cramming for. If you stick with D&D for awhile, you'll be going back to that book for years and what's important to you [that you have a hard time remembering, or really enjoy showing other people] will change with time.

The point of the tags is to mark the starts of chapters or specific topics in the chapters so don’t waste time flipping pages to find the section. Not for marking each idea.

Some of the respondents are right, highlighting is a technique for identifying "the main idea" or "key information" but the text of the PHB is largely written with such concision it's all going to be releveant at one point or another.,  Using stickies or more permament tabbing is probably good to guide you to sections.  Beyond that I wouldn't mark it up outside of taping in errata or just using own annotation for that or optional rules you supplant from the RAW in game.  

I haven't done it myself, but I would mark up in pencil or ballpoint, I don't trust the paper to handle gel ink or whatever else highlighter would do from bleeding through the other side of the page or transferring to the facing page.  I've got some questions about D&D 5e books, speaking of the materiality of texts, like they literally smell different from every other book I own, game or not.  It's the same smell with every book.