You should own a dictionary, a thesaurus, and a usage manual. You should read some style guides but not necessarily own one. Dictionaries While you can get quite far with a collegiate dictionary, serious writers (and serious readers) will want an unabridged dictionary. Among modern dictionaries, I like the American Heritage Dictionary of the English Language. (There was and may still be a free version online at bartleby.com.) The great classic American unabridged is the Webster's Second International, but it's expensive and old. Avoid the permissive Third International. Online, Webster's Revised Unabridged from 1913 is surprisingly useful.
The Concise Oxford English Dictionary has great entertainment value, but I find it less useful as a resource for the working writer, though the examples can sometimes be helpful to find out how words are used, e.g., with what prepositions. Thesauri A thesaurus is an essential tool to help you find the right word. Get Roget form; a dictionary-form thesaurus is useless. You can get an ancient but still useful Roget thesaurus from ARTFL. Usage Manuals This kind of reference tells you what kind of English is correct and what isn't. The best books in this category, like Fowler or Strunk and White, also tell you what is good style.
The Dictionary of Modern English Usage, written by Henry W. Fowler and revised by Sir Ernest Gowers, is the classic by which all other such manuals are measured. Although ostensibly in dictionary format, so you can look up particular points of usage, it is best read cover to cover (a good ten-year project). Try looking up Elegant Variation. You can see reviews at amazon.com. You want the second edition, revised around 1956. Avoid the evil third edition, which is a disgrace and a ripoff. Fowler must be spinning.