Short answer
For new players, Stanton is usually the most obvious entry point because it is more controlled, more accessible and more understandable than Pyro. Pyro is rougher and more dangerous. Nyx is especially interesting for beginners as a Lore and future context; check current RSI information before you assume that individual places are currently playable.
Game world and its places
Star Citizen does not consist of a single map, but of several star systems with very different moods. Some places are controlled, economical and civilized. Others are dangerous, raw or largely outside state control. These differences make the "verse" exciting for new players: you not only get to know missions, but also places with your own atmosphere.
Stanton
Stanton is the most important entry point for many players. The system is strongly influenced by large corporations and acts like a mixture of industrial area, megacity, commercial space and private business sector.
For beginners, Stanton is relevant because you get to know many basic processes there: space ports, landing zones, stations, simple missions, trade, industry and the first longer flights. It becomes more difficult, especially in big cities, because paths, performance and orientation can quickly be overwhelming.
ArcCorp is an extremely urbanized world. The surface is strongly influenced by city, industry and infrastructure. Area18 is one of the most famous places and conveys very well how dense, loud and commercial Star Citizen can work.
Hurston is harsher and more industrial. The planet belongs to Hurston Dynamics and is more synonymous with factories, weapons industry, environmental pollution and hard working conditions. Lorville looks correspondingly heavy, dusty and less inviting than other places in the system.
Crusader is a gas giant with a special atmosphere. Instead of classical land masses, floating platforms and the city of Orison stand in the foreground. Crusader feels brighter, airier and more elegant than Hurston or ArcCorp.
microTech is cold, modern and technological. New Babbage looks cleaner, more futuristic and more orderly. The planet offers strong contrasts of high-tech architecture, snow, ice and wide landscapes.
Pyro
Pyro is the much tougher antipole to Stanton. The system is unclaimed, more dangerous and strongly characterized by outlaws, fractions and survival struggle. For beginners, Pyro is therefore not simply "another system", but an indication of how different Star Citizen wants to shape its places.
As a new player, you should consider Pyro as a more advanced area. It can be very atmospheric, but requires more caution, better preparation and more realistic expectations of security, supply and technical stability.
Pyro I is close to the star and stands for a harsh, extreme environment. The planet is less a pleasant starting point than an example that not every celestial body in the verse should be comfortable or inviting.
Monox, also Pyro II, has an atmosphere that is only limited to life-friendly. The planet conveys well that "accessible" does not automatically mean "safe". Places like Monox should feel more dangerous and less controlled than the known landing zones in Stanton.
Bloom, i.e. Pyro III, is the more friendly counterpole within the system. It is considered to be more life-friendly than many other places in Pyro and shows that even a dangerous system must not only consist of empty rocks and ruins.
Pyro IV is particularly interesting because it no longer functions simply as a classic planet, but is described as an outer moon of Pyro V. This makes Pyro astronomically and atmospherically much more alien than Stanton.
Pyro V is a gas giant with several moons. The system around Pyro V looks large, remote and dangerous and fits well with the general character of Pyro.
Terminus, also Pyro VI, is one of the most important places when it comes to the harsh, lawless character of the system. In the vicinity of Terminus, fractions, stations and survival spaces play a greater role. Pyro feels stronger than a border area in which security is not a matter of course.
Nyx
Nyx is another important system and is clearly different from Stanton and Pyro. It is located on the edge of a dark fog region and is also unclaimed. This makes Nyx less like an orderly economic area and more like a place for people who want to live outside the reach of the UEE.
For beginners, Nyx is especially important to understand the breadth of the Star Citizen game world. Treat details about Nyx, Delamar and Levski cautiously: Some places are strongly associated with Lore, previous game levels or future content and can change in the Alpha history.
Nyx I is a special planet because it is connected to terraforming and experimental technology in the Lore. It stands for the long-term, still unfinished character of many places in the Star Citizen universe.
Nyx II is a smog planet with a toxic and corrosive atmosphere. It is not a classic adventure planet, but a harsh, life-defying place that shows how different the celestial bodies can be in the verse.
Nyx III is an ice giant and forms the outer large planetary counterpole in the system. It shows the rather cold, remote side of Nyx.
Delamar is particularly important in the Glacier Ring. There is Levski, an independent settlement created from an old mining plant. Levski stands for a different type of Star Citizen: less high gloss, less corporate world, more peripheral area, resistance and life outside official structures.