How do I combat players at 1500-1600?

"... thinking correctly in most positions takes time. Playing almost exclusively fast games obviously precludes practicing correctly, and so you will never get very good! Sure, fast games are fine for practicing openings (not the most important part of the game for most players) and possibly developing decent board vision and tactical 'shots', but the kind of thinking it takes to plan, evaluate, play long endgames, and find deep combinations is just not possible in quick chess. … for serious improvement ... consistently play many slow games to practice good thinking habits. ... I know that a large percentage of my readers almost exclusively play on the internet - after all, you are reading this on the internet, right!? But there is a strong case for at least augmenting internet play with some OTB play, whether in a club or, better yet, a tournament. Tournament play gives you the kind of concentrated, slow chess that often helps improve your game, especially if you are inexperienced at slow play. I would guess that players who have never played OTB usually gain 50-100 points of playing strength just from competing in their first long weekend tournament, assuming they play five or more rounds of very slow chess. ... Sure, an occasional weekend event takes a lot more of your time, but the benefits are comparatively greater if improvement is your ultimate goal. Don't have two day? Try a one-day quad (a round-robin among four similarly rated players). How often should you play? ... A minimum of 8 OTB tournaments and about 100 slow games a year is a reasonable foundation for ongoing improvement. ... Can't make 100? Then try for 60. If you only play three or fewer tournaments a year and do not play slow chess regularly at a club (or on-line, where G/90 and slower play is relatively rare), then do not be surprised that you are not really improving. ..." - NM Dan Heisman (2002)
https://web.archive.org/web/20140627052239/http://www.chesscafe.com/text/heisman16.pdf

With little money, it is particularly important to make sure that every purchased book is right for you. Before buying, pay careful attention to any available online reviews and samples.

"... If it’s instruction, you look for an author that addresses players at your level (buying something that’s too advanced won’t help you at all). This means that a classic book that is revered by many people might not be useful for you. ..." - IM Jeremy Silman (2015)
https://www.chess.com/article/view/the-best-chess-books-ever