Years ago I studied in a Belgian university. I was taking a medieval Latin course, and the professor, who was quite a character, had just returned from Rome, where he had worked in the Vatican Library. There he was horrified to see researchers taking notes on laptop computers. In class, telling us about this abomination, he threw up his arms, and announced in a shriek, "Les americains, ils sont des barbares!" ("Americans, they are barbarians!"). Arms still in the air, he looked down at me--I was smiling beatifically, of course--and he said peremptorily, "Pas vous" ("not you"), and then he repeated his earlier proclamation even more loudly. I recall this comedy every time I pull out my laptop in an archive.
The whole question of how to transcribe documents is actually not simple, the reason being that most handwritten (and early printed) material used abbreviations and had an odd and irregular punctuation system. If one takes notes by hand, it is easy to reproduce the abbreviations. Though, of course, sometimes in the reproduction the abbreviation gets a bit mangled, causing problems later. However, taking voluminous notes longhand and in pencil can be tedious, and it's not searchable and might have to be typed out anyway later.
That might argue for using the computer, but that has its own problems. First, you have to turn off autocorrect or be very conscious of the word processing program automatically changing the spelling. Second, you have to decide whether you will expand the abbreviations and use square brackets to show that or try to reproduce the abbreviations. If the former, you have to be sure you are correct. If the latter, you need to establish a constant rule for what computer symbol represents what abbreviation symbol, and you need to make a key, so that you don't forget. You also should decide on a rule for using "[sic]." Depending on the text, I tend to use [sic] when the spelling is such that it might look like a typo, e.g. intirely for entirely, and I want to remind myself that it is not.
There can also be a problem deciding what letters are capitals. The initial "s" for some reason in a lot of the 18th-century documents I've used can be written large or small, and it's not always easy to tell if the writer intended it to be a capital. When I encounter that sort of problem, I look through the document and try to determine what a true capital "s" (for instance) looks like, then I make a rule about how I will transcribe the letter, and I stick to it throughout the document. Also, it is always a good idea to make lots of notes about what you do with a document. For instance, most documents have some kind of text on the verso. I will transcribe that as well, or at least note it. And if there is nothing, I will note that, too. It is tempting when in the archive to think that you will remember what you see. Archival work is very "in the moment," and so you always feel as if your memory will be vivid. But it won't be. And I hate the feeling later of wondering whether I missed something because I don't have an indication in my notes that I checked the verso or made observations about other characteristics of the document or the like.
Finally, as the medieval scribes knew, it is impossible to copy out a text without introducing errors, so whether you type or write, it's necessary to do a word-by-word proofread. If I have not attempted to reproduce the punctuation and abbreviations exactly, I note that on the text. If I have, and I have checked the text carefully, I write at the end: "checked and corrected." If all I have done is reread the transcription looking for obvious errors, I write only, "checked." Even if I think I have proofread the transcription carefully, a later rereading almost always shows that I missed something, so I try to reread the text again afresh while I still have the possibility of returning to the archive to double check my work.
In any event, I do not have a hard and fast rule for handwriting or computer. It depends on the document, its length, and the complexity of transcribing the abbreviations. The more abbreviations, the more likely I am to hand write.
