301 Wheel Set
General Information
The following information has been collected from original newspapers, catalogs, and magazines, some of which are freely available for reference below. The rest can be found in the site’s gallery. No aggregate catalogs (BrickLink, Brickset, etc.) were used.
Instructions: H-2228
Advertised Part Count(s): 301 pieces
First Year Confirmed Available: 1966 (USA)
USA Only. Sears exclusive from 1966-68, then from late 1968-1971 was used in Kraft promotions. This article is largely for the Sears version, the Kraft version will be elaborated upon in the articles covering the Kraft promotions.
Most Likely Retirement Date: 1971
While likely a slightly different assortment, the 301-piece set seen in the 1971 Kraft Brochure is essentially the 301.
Last Year Seen Available: 1971
Aliases: Wheel Toy Set, Wheel Set, Set No. 3, Set No. 8
Retail Price(s): $5.00 - $6.50 (USA)
Note that the case variant sold for $12.88
Rarity Score (Rarity Index): 5/7
Known Box/Packing Variants
There are two main variants, though if you really want to get into the weeds, there are four.
Three of which are the plain box versions available through Sears and Kraft. The main difference is that the Kraft ones will have a shipping label on it with "Kraft/LEGO Special Offer", and it will have different set numbers depending on if it came from 1968-1970 or 1971. The inner trays could also differ in 1969+ copies, instead using the one-piece gray tray, but that is just speculation.
This is the Sears 1966-67 one, identifiable via the catalog number on the side:
Then there is the Sears version from 1968, sold in a Samsonite LoveLand case. It is notoriously difficult to identify in the wild when compared to other Samsonite blue case sets (i.e. the 1968-70 Kraft Set No. 4 or the 1968 Treasure Chest), unless it still has its unique instruction sheet:

Box/Overview
The 301 Wheel Set (or Wheel Toy, depending on which catalog you're referencing) released as a Sears exclusive in 1966 and as covered above, went on to be used in the Kraft promotion from 1968-1971. All these used the plain mailer box, except for the Sears case set in 1968.
Beyond its relative rarity, there's a lot about the 301's story in a larger context that I find particularly fascinating. It seems to be just another Samsonite set, but as we've found before, these later sets were derivative, not their own independent entities appearing in a vacuum.
We've covered this extensively elsewhere, but the 1965 wave of sets was largely a repackaging of the older sets:

We've already accounted for the 702 Small Basic Set with the 93-Piece Set, so notice what's left: the 610 Super Wheel Toy.
The 610 was the only 1961-64 set to continue production into 1965, being the only set pictured among the new wave of sets:

And that association carried over even with promotional images in 1965:

So the ~300 pieces of the 610 matches the 301 really well. The prices, however, do not (compare $6 to $10). And I'm not really sure why that is. The 301 is a completely different assortment (mainly demonstrable by the shift from primarily blue parts to red/white, as well as excluding the larger 4x4 wheel), but that usually wouldn't warrant such a drastic difference.
But the 301 isn't the only set to match the 610's DNA, as we have a "298-piece Deluxe Wheel Set" in the 1968 Parade Promotion, the only known appearance of several promotional sets:

Which shows a much stronger candidate for the 610's continuation (as it uses the larger 4x4 wheel and the name "Deluxe Wheel Set" better follows the evolution from "Super Wheel Toy"), but even the $7 price here doesn't exactly match the 610's. The price doesn't necessarily have to match, we see as sets in the 1965 wave got bigger they were able to reduce the price, but the difference here should be noted as a limitation due to the complexity of the subject.
There's also the missing provenance for the 298-piece set from 1966-67, while the 301 has that and matches perfectly, Super Wheel Toy from 1964-65, then 301 Wheel Set from 1966-67 through Sears. Sears switched to the plastic attaché case in 1968, still advertising exclusivity, the same year the Kraft promotion began with a 300-piece wheel set.
There really isn't a resolution to this to date, but there will likely never be. Recreating internal logic is hard to prove definitively, especially when accounting for every last detail.