120 Basic 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.
Advertised Part Count(s): 120 pieces
First Year Confirmed Available: 1965 (USA)
I’ve written an extensive article about the US 1965 wave in particular.
Canada carried a similar (but different) numbered version called the 125 Beginner's Set.
USA Only.
Most Likely Retirement Date: 1971 (USA)
The 120 set was a permanent member of the basic set line introduced in 1965 and was in continuous production until the cancellation of the LEGO license. It appears in an idea book used throughout 1970-1971.
Last Year Seen Available: 1972
Transcript Telegram, July 15th, 1972
Aliases: 120 Piece Set, No. 120 Basic Set, Starter Set, Beginners Set
Retail Price(s): $2.95 (USA)
Discounted Example(s): $1.59 (1966), $2.33 (1969), $1.33 (1971)
Rarity Score (Index): 1/7
Known Box/Packing Variants
As with other 1965 sets that were produced into 1971, the 120 Basic Set has several box variants. Note the list below is likely not exhaustive:
The 1965-66 waves will have a drawer/sleeve style box, two patents, and "AGES - 3 TO 8":

Then in ~1967-68, it had a drawer/sleeve style box, two patents, and "FOR ALL AGES":

In ~1968-69, it had a drawer/sleeve style box, eight patents, and "FOR ALL AGES". ~1969-70 had the same box front, but the box was tabbed and transitioned over to the single-piece gray tray. "Starter Set" began appearing on the set's sides as well:
Then for ~1970-1971, it was given a tabbed box/single piece gray tray and has "Some parts...produced in Denmark" printed directly on the box. 1970 examples will have it stickered:

It probably did not have a mailer variant. The 120 should not be confused with the Sears exclusive 151-Piece Set or the Canadian 125 Beginner's Set.
Box/Overview
At its release in 1965, the 120 Basic Set was the smallest set available at normal retail. It both had more pieces and cost $1 more than the smallest set for the 1961-65 wave: the 702 Small Basic Set. The 120 set more aligns with the 703 Basic Set's part count (126 pieces) and price ($2.95).
The 120 Basic Set carries a similar design as other basic sets from 1965. The one shown below is a later variant, but the presentation is universal:
Below is the drawer:
And the back featuring models that can be built with the parts included in this set:
Speaking of the parts in this set...
Contents
As usual, the image shown below is a general guide, not to be taken as law.
The example pictured below is from 1965, evidenced by the inclusion of cellulose parts and the outer sleeve. By 1966, the inventory of cellulose pellets had been entirely depleted (except for yellow).
The most surprising part for me is the inclusion of a paper tray. It doesn't seem to be a later addition because all the trays were originally glued, and the paper tray is also glued (which is a distinctive feature of 1965 sets). As paper trays are much more common with later examples (~1970), it may be that paper trays were used throughout 1965-71 as a substitute when stock ran out.