Dutch dictionaries
Dutch language in the 17th century
In the 1600's the Dutch language was beginning to modernize. The Republic shed Spain finally in 1648 with the Peace of Munster and was recognized not only as an independent country but also as a world power. Growing consciousness of Dutch as a shared language was a crucial part of that process.
J. M. van der Horst's overview "A Brief History of the Dutch Language" from The Low Countries. (4:1996-1997) (my emphasis):
Broadly speaking, the Dutch language acquired in the sixteenth and seventeenth centuries those characteristics which it still has today. The original Germanic case system, still present in Middle Dutch, disappeared after the sixteenth century. In this respect Dutch is more like English, in which the cases also disappeared after the Middle English period, whereas German has preserved its cases into the present time. In fact this difference from German was apparent very early: in Old Dutch dative and accusative tended to fuse, while in Old High German they remained distinct, as they do to this day in modern German.
On the other hand, Dutch developed a word order that is closer to German. Unlike in English the verbs are not all placed together. In main clauses the conjugated verb is in the second position, and the remaining verbs are at the end of the sentence. Dutch also has a different word order for dependent clauses.
In addition, Dutch has its own special characteristics, such as a future with zullen and gaan, a passive with worden and zijn; two genders for nouns (de and het) compared with the one (the) in English and the three (der, die and das) in German; and highly developed use of prepositional adverbs (erin, daarop, waardoor, etc.) which certainly do exist in English and German but enjoy only marginal use in those languages.
Finally, the Dutch vocabulary contains fewer Romance loan words than English, but more than German.
Extensive overview: Wikipedia's History of the Dutch language
Antony van Leeuwenhoek wrote in early modern Dutch, so an understanding of today's Dutch lets you read most of the writing of van Leeuwenhoek and his contemporaries.
Dictionaries from Leeuwenhoek's time
The two major Dutch-English dictionaries of the time bracket Leeuwenhoek's career.
In 1648, Hendrick Hexham (1585?–1650?), an ex-soldier, published Het Groot Woordenboeck, the first Dutch-English / English-Dutch dictionary, including a grammar. The English-Dutch part was published in 1648 and the Dutch-English part in 1658, both in Rotterdam by Arnout Leers.
The DBNL (Digitale Bibliotheek voor de Nederlandse Letteren \ Digital Library of Dutch Language and Literature) has made a downloadable and searchable PDF of the 1675 edition, amended and enlarged by Daniel Manley, available at Google Docs. A version is available for download at Google Books.
Dictionaries Today
Van Dale's is the standard Dutch-English dictionary (two blue volumes below). It is especially strong on usage of the terms in phrases that help distinguish the subtle but important differences. I use the version that I downloaded to my computer. If I enter a verb form, it shows the infinitive form.
Van Dale Groot woordenboek Nederlands - Engels : Van Dale Comprehensive Dutch - English Dictionary (Dutch Edition) 4th edition (October 1, 2008)
Grammar
Donaldson's Dutch grammar (red cover below) is the best I have found written in English.
Donaldson, Bruce. Dutch: A Comprehensive Grammar (paperback | hardback). New York: Routledge, 2008
The best online grammar site I've found is DutchGrammar.com, which has a grammar reference, also downloadable, audio files to help with pronunciation, and a forum where many nuances get explained.
Verbix's Verb conjugation on-line - Dutch - is helpful for writing.