Poland is pretty set between the east and west of Europe. What led to Christianity and the Latin alphabet winning our over Eastern Orthodoxy and the Cyrillic one?
The answer to the question about the reasons why the lands that will later become Kingdom of Poland adopted western form of Christianity is definitely multi-faceted, but one of the factors seems to be predominant and it is the physical location of the area in question. Lands ruled by Mieszko I, the first historical ruler of Poland (not the first king, this honour will be granted to his son, Bolesław I), were at first largely limited to what is now central Greater Poland and Kujavia, with rivers as natural borders: Odra in the West, Noteć in the North, Vistula (up to Płock) in the East and Barycz in the south, and later were expanded by the land of Chełmno in the north-east and the land of Sieradz and Łęczyca in the south-east. In the mid-10th century this area was thus bordering with Upper Lusatia vassalized by German king Henry I, Lower Lusatia incorporated to Saxon March by margrave Gero (vassal of Emperor Otto I, son of Henry I) and Silesia, that since the dissolution of the Great Moravia has been controlled by Kingdom of Bohemia. Thus, lands controlled by Mieszko I in the early 960s were bordering with two large Christian powers that were also followers of Western Christianity, i.e. Roman Catholicism.
Conversely, the influence of Eastern Christianity (Eastern Orthodoxy) was limited by the distance from Orthodox lands. In the east, Mieszko's domain was bordering with pagan Slavic areas that will be incorporated by Mieszko and his son Bolesław into what is now Poland over the course of their reign. Further east there were Ruthenian principalities that were also pagan (Kievan Rus' will be baptized only in 988). Contact with the areas located further to the southeast was limited due to the natural barrier that was the Tatra Mountains, an alpine mountain range, to a large extent protecting the northern Slavic lands from the Magyar raids. Nevertheless, the closest Orthodox polity was the Transylvania, where local ruler (known as Procui or Julius, although the latter is thought to be a misunderstood rendition of his official title of 'gyula', roughly equivalent to 'prince') accepted Christanity at the hands of the Eastern Roman Emperor. His domain was however relatively small and of little importance in comparison with Germany or Bohemia, not to mention quite distant. Thus, the contact between Mieszko's lands and the seat of Orthodox Christianity or any Orthodox country was far weaker than in the case of Kievan Rus' or Southern Slavic polities.
In addition, some scholars posit that Mieszko I did not necessarily need to be a pagan. There are suggestions of a possibility that Mieszko could have been a member of the Moravian Moymirovic family and thus could have been baptized in his youth, and then was only officially recognized as a Christian leader in 966. This theory is based on an observation that the country of Polans has already been well-developed for the 10th century standards and shows various traits of a state as such, not just a loose federation of the local communities, what is interpreted as a possible proof of the political knowledge present in the territories south of Poland (Bohemia, Moravia) but not present to the north (Scandinavia), immediate West (lands of Veletes and Obodrites) or East. Additionally, the baptism itself is not really mentioned in any contemporary chronicle and was most likely not a well-known event. In early 970s, Widukind of Corbea in his Res gestae saxonicae presents Mieszko as a still pagan leader (although a 'friend of the Emperor'). The first mention of the baptism can only be found in Thietmari merseburgiensis episcopi chronicon written by Thietmar of Merseburg in the second decade of 11th century, while the first sources from the territory of Poland have been written only a full century after the fact. The issue is further complicated by the fact, that the ruins of a castle with a chapel located in the Temple Island in Poznan have been carbon-dated to 'after 941', full 25 years before alleged date of baptism. Of course, we can't just dismiss the possibility of a dating error and the fact that relevant sources might have existed but simply not survived (and given the turbulent history of the area in the 11th and 12th century, especially the devastating incursion of Brzhetyslav I in 1038, it would have not been at all unusual), but the controversy is legitimate. It is also possible that the baptism of Mieszko would have not been considered a great event, because his land was not exceptionally large, strong or important, especially in comparison with Kingdom of Bohemia in the south or even the Veletian Confederacy.
Although the reason for the adoption of Christianity through Bohemia is often given as an attempt to avoid forceful Christianization by Germany, in the recent decades such approach started to be treated as the post-18th century projection of anti-German sentiments chiefly fueled by the Partitions and relatively harsh measures taken to promote German language and culture over Polish in the annexed lands (and later also supported by the anti-German attitudes resulting from the Second World War). Today, however, historians tend to point that the relations between the first members of Piast dynasty and Czech rulers were generally more strained than relations with rulers of German lands, with Silesia, located right between Greater Poland and Bohemia being the main bone of contention, while according to the aforementioned Widukind, relation between Polish ruler and Holy Roman Emperor were amicable. It is possible that the alliance between Mieszko and Boleslav I, duke of Bohemia, that eventually led to the baptism of the former could have been an attempt to gain an ally, as Boleslav declined to pay a tribute to German king what created tensions between these two states and a punitive military action against unruly Bohemian duke was a real threat. Nevertheless, Thietmar of Merseburg attributes Mieszko's conversion to the influence of his wife, Dobrava, daughter of Boleslav I. According to him, she has been married to a still pagan Mieszko and only later persuaded him to accept Christianity. On the other hand, Gallus Anonimus, a chronicler living in Poland in late 11th and early 12th century wrote in Cronica et gesta ducum sive principum Polonorum, that Dobrava and Mieszko only married after the baptism of the latter, although historians tend to trust Thietmar more. By the way, the idea of cooperation between Christians and pagans was not that unusual in that part of the world. In 13th and 14th century, largely Orthodox Russian dukes joined forces with pagan Lithuanian rulers, and Poles were supporting pagan Prussians against Teutonic Order that was not above procuring help of vaguely pagan Lithuanians.
So, to sum it up, the area that will later become Poland adopted western Christianity because its leader had very good contacts with the states that were already Catholic, while the presence of Orthodox Christians in this part of Europe was rather scarce (we do not know, if the first members of Piast dynasty knew of Orthodox Christianity and even if they did, they could have not treated it as a separate faith). Thus, regardless of whether the decision concerning baptism was motivated by the political alliances, spiritual considerations or adoption of Western culture, Mieszko had many opportunities to do so and the benefits were obvious and immediate, as the status of a Christian ruler could have helped to tighten the relations with his neighbours. Thus, the only reasonable and practical option for baptism was an adoption of Western Catholicism.