The beginnings of this series are hazy, although it's possible to make some educated guesses. The index to volume 167 (January to June, 1955) of Publishers Weekly lists an announcement of a higher-priced line known as Gateway Editions on pages 2776 and 2880; unfortunately, the issues from June 1955, in which those pages would've appeared, are not available in the Publishers Weekly Archive. A later reference suggests the announcement came in the June 18, 1955, issue. A note in the Feb. 18, 1956, issue of PW, at 1031, suggests that Regnery will devote more promotion to the new Gateway Editions line, "introduced last fall" with 12 titles. The note indicates 16 more titles would follow, presumably in 1956.
Looking further back time in the PW Archive, however, there are hints at predecessors. For instance, a note in the Sept. 19, 1953, issue, at 1181, says that Regnery has a mailer "listing the books in the firm's series of inexpensive classics, Gateway College Readings." My suspicion is that the phrase "Gateway College Readings" was a promotional slogan related to the titles Regnery published in conjunction with the Great Books Foundation. Perhaps Regnery simply used the "Gateway" moniker in marketing prior to the formal introduction of a numbered series like the one I have in mind here.
Case in point, there's a Weekly Record entry in the May 15, 1954, issue, at 2105, for a "Gateway ed." of Plato's Euthyphro, Apology, Crito and Symposium in paperback at $.80. This title for sure was published as a Gateway Edition with the series number 6002 at some point; perhaps Regnery's early Gateway titles appeared before the actual series was conceived of or begun. Some publishers apparently did this, probably forming series from extant paperbacks to cash in on the quality paperback boom of the mid-1950s. See also a reference to discounts on Gateway Editions from the July 24, 1954, issue, at 370, clearly predating the PW writeup of the series's introduction. I'm giving the early titles years that predate the actual Gateway Editions series. I fully suspect that the titles that first appeared prior to fall 1955 did not have series numbers until later printings, but I can live with that.
From preliminary research, it seems as though the series starts at 6001 and proceeds higher, title-by-title, through the 6090s (1965). Sometime in the late 1960s/early 1970s, the numbers for Gateway Editions stop being entirely sequential, although many do follow in order through the 6100s; that said, I found that 6098-6100 are out of chronological sequence (published in 1973, 1972, and 1973, respectively). I've also come across books published in this time frame, 1966-1973, that are not in the 6000-6100s range but are still Gateway Editions.
Here's what I think, based entirely on a hard day's night of supposition, happened. The series was chronological through the 1960s and into the 1970s, but there were some numbers that didn't have a title, for whatever reason (sometimes numbers are assigned but the release is delayed and occasionally no book ever comes out with that number.) Sometime around 1972, Regnery went back and published titles under previously unused numbers, like 6098-6100.
Enough said about Gateway Editions? Hardly. There's also a possibility that some of the Gateway titles from 1967 onward were part of a wayward sect of Gateway Editions, as there evidently was a great divide: some Gateway Editions were Classic titles and some Contemporary. This information comes from a small notice in the Dec. 26, 1966, PW, at 269. Despite this notice, I've not found any evidence from other sources or the covers themselves that there was a significant division of the Gateway Editions into two streams.
The Henry Regnery Company changed its name to Contemporary Books, Inc., effective May 1, 1977. By that point, Henry Regnery himself had been absent from the company for some time, according to then-president Harvey Plotnick, and the name change reflected a departure in direction from the Regnery-less company (All this according to Regnery Changes Name, Announces New Programs, PW, Apr. 18, 1977, at 28.)
By the end of 1977, Henry Regnery had purchased the paperback backlist from his former firm, now Contemporary Books, Inc., and had formed Gateway Editions, Ltd., based in South Bend, Indiana. This newly-formed company republished many of the Gateway titles from the Regnery Company backlist (see Gateway Editions, Ltd., ad in PW, Aug. 29, 1977, at  for a full list of titles with ISBNs.) I'm not concerning myself with this Gateway 2.0, as they seem to lack any semblance of order as a series. By early 1979, Regnery had changed the Gateway Editions, Ltd., name to Regnery/Gateway, Inc. The firm continued to offer Gateway Editions well into the 1990s and beyond.
167 PW 2776, 2880 (1955) (announcing the higher-priced Gateway Editions -- n.b. the PW Archive has no articles from June 1955).
PW, Dec. 26, 1966, at 269 (announcing division of Gateway Editions into two sets: Classic and Contemporary).
Regnery Changes Name, Announces New Programs, PW, Apr. 18, 1977, at 28.
Gateway Editions, Ltd., ad in PW, Aug. 29, 1977, at .
News of New Publishers: Gateway Editions, PW, Nov. 21, 1977, at 22.
Name Changes: Gateway Editions, Ltd., PW, Mar. 5, 1979, at 29.