Old English, Middle English, and Modern English are almost entirely different languages. Old English and Middle English no longer have any native speakers, and are considered dead languages, studied only by historians and academics. Old English is not recognizable to Modern English speakers in any way today, except for maybe one or two words in isolation.
For example, this is a sentence in Old English:
We Gardena in geardagum, þeodcyninga, þrym gefrunon, hu ða æþelingas ellen fremedon.
This is very easy to distinguish from Modern English, as it uses letters of the alphabet that do not occur in Modern English, and is said to be closer to German than it is to modern English. In this sentence, I can recognize roughly three or so words that have remained mostly intact: "We", "in", and "hu" (which is spelled "who" in Modern English). If someone were to tell you that the ð letter is pronounced like "th", you might be able to see that ða is "the".
Other than these, it is a completely different language.
Middle English is also a different language, although it is slightly more understandable by Modern English speakers. Here is a sentence in Middle English:
And so bifel, whan comen was the tyme of Aperil, whan clothed is the mede with newe grene, of lusty Veer the pryme, and swote smellen floures white and rede.
The biggest difference between Middle English and Modern English is something called "The Great Vowel Shift". The sounds vowels made suddenly changed at some point some several hundred years ago. If you look at these words and change the vowels around, you should be able to understand the majority of the words. Some words will still be unreadable, but most of the words are okay.
Bifel → befell, whan → when, comen → come, tyme → time, Aperil → April, mede → meadow, newe → new, grene → green, and so forth.
Middle English will often look like Modern English that was heavily misspelled. If you listen to someone speaking Middle English, it will sound nothing like Modern English, but reading it is just barely possible with a lot of effort.
Modern English is what we are writing right now. I assume you can recognize this because you are studying it. There's also "Early Modern English", which is sometimes mistaken for "Old English" because... well, it's several hundred years old. "Early Modern English" can be recognized by the use of additional pronouns such as "thee" and "thou". The famous playwright Shakespeare wrote in Early Modern English, even though by his time, some of the words were already "old fashioned".
Shall I compare thee to a summer's day? Thou art more lovely and more temperate.
Regarding which of these three languages is preferred? Again, Old English and Middle English are both dead languages. No one but scholars and historians speak them at all. Modern English is highly preferred. Early Modern English can still be used poetically if you really want to, but it isn't preferred by any means.
I am not certain, but you may instead be asking whether words derived from Old English or Middle English are preferred? And the answer is no. Once a word is in Modern English, the root of the word does not matter. That said, words derived from Old English are more likely to be "common" or "casual" words, while words derived from French are more likely to be "formal" words. This is merely a tendency, not a hard rule though. You really do need to look at Modern English words on a case by case basis.
