This is a surprisingly complicated subject, because Revell actually made two Mayflower kits. I normally regard Thomas Graham's book, Remembering Revell Model Kits, as the bible on the subject, but (as Dr. Graham has graciously acknowledged in this Forum), this is a rare example of a piece of detail that he missed.
The first kit was originally issued in 1966. (I'm confident that Dr. Graham's date is correct.) It was about 16" or 18" long; I think the scale was somewhere in the vicinity of 1/110, or maybe a tiny bit bigger. (I remember that the Pilgrim figures in the kit were smaller than those in the 1/96 Constitution and Cutty Sark kits, and certainly appeared to be in scale with the rest of the model.) The kit came in the same size box as what my generation thought of as the "$3.00 kits" - the Bounty, Victory, Santa Maria, Eagle, etc. (I think it probably cost $4.00 or $5.00 when it was initially released; they'd all gone up a bit by then.)
A few years later Revell released a small series of "Quick-Build" sailing ship kits, which were designed to attract newcomers to the hobby - and to occupy a "price point" between the big 3' kits and the smaller, 18" ones. Three of them (the Constitution, Cutty Sark, and Thermopylae) were scaled down, simplified versions of larger kits. One, the yacht America, was a brand new kit. And the Mayflower, oddly enough, was an enlarged version of the earlier kit. It was advertised as being "simplified," but in fact the only changes (beyond the enlargement) were the omission of all the rigging blocks and the replacement of the wretched plastic-coated-thread "shrouds and ratlines" with even worse injection-molded plastic parts. This, I'm pretty sure, is the kit that's on 1/83 scale. With the bowsprit attached it was about 2' long, or close to it.
Later still, Revell re-released the original, smaller kit in a "Quick-Build" box. This was the original, smaller kit, with the rigging fittings omitted and injection-molded "shrouds and ratlines." Anybody who's confused at this point is not alone. I think I have the story straight - but I'd be lying if I said I was sure.
At any rate, I'll stick my neck out and offer the opinion that both these kits are, in terms of historical accuracy, among the dozen or so best plastic sailing ship kits ever. They are indeed scale models of the Mayflower II, the full-sized reconstruction that crossed the Atlantic in 1956. She was designed by William A. Baker, Professor of Naval Architecture at MIT and one of the best in the business. Mr. Baker made one deliberate compromise with reality: since the ship was destined to be a floating museum and tourist attraction, he added a couple of feet of extra headroom below decks. Otherwise, in the more than 50 years since he drew the plans for her, nobody, to my knowledge, has suggested that he made any major mistakes. (Caveat: we know so little about the real ship that there's plenty of room for interpretation as to what she looked like. Several other people have drawn plans that look a little different from Mr. Baker's. But I've never read any serious, qualified assertion that his version isn't reasonable.) That includes the color scheme.
Mr. Baker wrote a book in which she's prominently featured: The Mayflower and Other Colonial Vessels. It contains a good set of plans, including a sail plan. (I've looked at the one Powder Monkey mentioned; it looks good too, though the one in Mr. Baker's book has more detail.) Anybody tackling any of the Revell kits can do no better than to get hold of a copy of that book.
Either of those kits has the potential to be an outstanding scale model. Good luck.