Collecting First Editions of her published books is arguably the starting point for many Christie collectors. With the first book published in 1920 and new first editions still appearing (though generally short story collections), the attributes of a correct first edition vary significantly. Generally, a collector needs to consider one of three lines of collecting firsts: (a) UK firsts (potentially including Colonial Issues), (b) US firsts, (c) actual first printings, regardless of country. The latter will include certain books that were published only in one country, providing variants not found elsewhere.
The fact that multiple avenues can be chosen in building a collection is reinforced when considering the options for her first novel, A Mysterious Affair At Styles. It was first published in New York, US, by John Lane in October 1920. The second known national printing was the Canadian version, by Ryerson, also in 1920 (likely November), using the US text plates but a different title page and slightly different binding. The UK version, published by Bodley Head did not occur until late January 1921, and had completely different text plates and binding. Print runs for these books were all small, likely a few thousand at most in the US and Uk, and the Canadian version is estimated at 300 based on comparable runs for other authors at that time.
Generally, the UK book was printed first but there were numerous instances when this was not the case, such as Murder in Three Acts (Dodd Mead, USA, 1934), while the UK version, Three Act Tragedy, was printing in 1935. The Moving Finger is another book where the US copy preceded the UK version by a year (1942 vs. 1943). Other books are only found in one country, for example, The Regatta Mystery (Dodd Mead, USA, 1939), was not published in the UK. There are even cases where the actual book is different. Five Little Pigs (Collins Crime Club, UK, 1942) is a significantly different book than the US version, Murder in Retrospect (Dodd Mead, USA, 1942), which is both significantly shorter and contains fewer characters. As this illustrates even trying to simplify the collecting route to a narrow path masks the complexities and fun of collecting Christie.
UK firsts are the most desirable to collect for a variety of reasons, including that they make up almost all of the true first printings, Christie was British and the print runs were often smaller than the US. Collectively, this makes the UK books rarer and more desirable, and thus more expensive in most cases. It also makes those from 1938 or earlier premier blue chip collectibles.
US firsts have compelling attributes making them desirable for collectors too. In almost all cases, US firsts are significantly more affordable than their UK counterparts, making it more financially realistic for many collectors to acquire them. The artwork on the jackets is different and in many cases the title was different. The natural evolution for many collectors in the States is to collect both, while those in the UK are more likely to collect only US books that were either published before the UK version or contain short stories not published there.