Very interesting question, but the answer depends on a lot of factors!

In terms of spoken language communication certain dialects of modern English would be more helpful in understanding certain historical forms of English.

18th century English would provide little problems for most modern English speakers, especially for the ones with a large vocabulary, as English has remained more or less stable for the past 250 years in both speech and writing. There exist phonographs (wax cylinders) containing recordings of spoken English from the 1870s; which are perfectly understandable. In terms of writing, the memoirs of the Duke of Wellington or a thesis by Isaac Newton, shouldn't create much difficulty either.

Prior to the 1700s however, it becomes more difficult because of the effects of the Great Vowel Shift; a series of changes in the pronunciation of the English that took place between the 15th and the 17th century. A few simple examples to give an impression of how the pronunciation changed could include; to bite (which would have been pronounced as 'beat/beet') and out which was pronounced as oot. For this form of the English language, it would help to be a native speaker of a particularly conservative English dialect; such as the West Country or Yorkshire dialect.

Nevertheless Middle English isn't incomprehensible to modern English speakers, especially in its written form because the spelling of words did not change nearly as much as the spoken language. This is why, compared to most other European languages, English has among the least phonetic orthographies. An example of Middle English from the 1400s would be Blyssid be the tyme that the appil take was, therefore we mown syngyn (translated: blessed be the time that the apple [from the Garden of Eden, red.] was taken, therefore we may sing) which would not be pose much of a problem to a speaker of contemporary English after some adjusting.

It's also important to remember that mutual intelligibility between languages is almost never symmetrical. Usually the speakers of language X can understand the speakers of language Y better than vice versa. This is especially true for closely related languages where one has simplified its grammar. For example Afrikaans is derived from Dutch, but Dutch is more conservative. For example, it has two articles whereas Afrikaans has only one; and it has a lot of irregular verbs, whereas all the Afrikaans verbs have become regular. This makes it easier for Dutch speakers to understand Afrikaans than it is for Afrikaans speakers to understand Dutch. The same principle holds for English and Middle English. A modern English speaker would have more difficulty understanding Middle English; but a speaker of Middle English would find it easier to understand Modern English.

When entering the realm of early Middle English or Old English; the game changes dramatically. The grammar, vocabulary and syntax of Old English are markedly different from modern English.

However, that isn't to say that it would be incomprehensible. The Germanic language family is quite diverse compared to most other Indo-European branches but some degree of intelligibility always exists. For example Danes can translate about 35% of German nouns; despite their languages belonging to different branches of the Germanic language tree. It would not be surprising for a speaker of Modern English to achieve similar numbers, especially concerning the most basic vocabulary and verbs.

In many ways, Old English would be easier to read than to understand while spoken; this is a common phenomenon in linguistics. It's often claimed on the internet that knowledge of German or Icelandic would help an English speaker in understanding Old English; or even that Germans and Icelanders would find Old English easier to understand than English speakers, but this is largely nonsense.

For one; German (even though it's the 2nd most spoken Germanic language) is a very a-typical Germanic language. Perhaps even the most "ungermanic" Germanic language spoken today; whereas Icelandic is a conservative North Germanic language, which presents other (phonological) problems when trying to decipher an old West Germanic dialect. A basic understanding of a case system (which does still exist in Icelandic and German) would be of some help though; especially because this will make the world order (syntax) of Old English seem more logical.

Could you understand the writer of Beowulf? It's highly unlikely you would be able to converse fluently or in any real depth, but, by using simple sentences and infinitive forms of (etymologically Germanic) verbs, you would be able to communicate; be it in a very basal setting.

After the Old English stage, when you would approach an early variant of West Germanic or even Common Germanic; communication would become very difficult though. These languages did not use prepositions, had a very expansive case system and had a highly divergent phonology, even more so when compared to English due to its Anglo-Frisian / Ingvaeonic features, which these forms lacked.

You'd last a little longer reading than speaking.

Speaking you'd make it to about 1500. Your accents would be thick and harder to understand, but you could get by. By the 1400s you start to sound funny, and when you reach the 1300s you'd need a lot of gesturing to get your point across. Anything pre 1100 would be essentially unable to be understood.

Writing you could go as far back as the 1300-1400s, when the writing would be spelled very weird, but context clues and some critical thinking would you get you right by. Example would be And that comyn Englysshe that is spoken in one shyre varyeth from a-nother which translates to And that common English that is spoken in one shire varies from another. Not so bad, right?

Anything from 1100-1300 (Chaucer) would be difficult to understand reading and practically a different language speaking. Before Chaucer, such as Beowulf, you'd have better luck speaking German or Norwegian to them.