Pick A League
(The details on this page are optional, but they're common questions and I would recommend reading it through. If you want to move along, however, the short version of this page is "play the current Challenge league, on Softcore, without solo-self-found enabled.")
One of the potential problems with a loot-driven game like Path of Exile is that you don't have very much fun once you've got the best loot in the game. Typically, games solve this in one of two ways: by frequent character resets, or by introducing new mechanics that enable even more powerful items. Path of Exile leans towards the first, but mixes the two, by introducing periodic Challenge Leagues.
Challenge Leagues contain separate economies and fresh characters, and you cannot transfer existing items into a league. Each of them also introduces some new game mechanic present only in the Challenge League, which is usually (although not always) added to the base game at the end of the League. The developers' stated goal is to release a new Challenge League every 13 weeks, although this is sometimes delayed, for a total of somewhat under four leagues per year lasting approximately three months each.
(Diablo players may recognize Leagues as the equivalent of Ladders from Diablo II or Seasons from Diablo III)
Completing special Challenges in a Challenge League (which vary from "trivial" to "extremely difficult and time-consuming") can reward special appearances for your equipment, Town Portals, or other mechanics that are only available through that league. Each League has 40 Challenges in total, and there are rewards for 12, 24, and 36 Challenges complete.
Most players play in Challenge Leagues, and thus restart from scratch every few months.
In addition to the Challenge Leagues, there is the Standard league. Characters in Standard are persistent and never reset, and as a result Standard contains items from all of Path of Exile's past content (some of which are now very rare or expensive) and has an extremely mature economy that can make it difficult for a new player to break through. Most players use Standard as a way to test new builds they'd like to try in an upcoming league without wasting resources, although dedicated Standard players do exist.
In addition to the regular Standard league, there is one other permanent league, the Hardcore league (see below).
At the end of a Challenge League, characters from that League are moved into Standard. You can continue to play them there if you wish, or you can restart anew in the next Challenge League.
Softcore & Hardcore Leagues
Each League, both Challenge and Permanent, has both a Softcore (technically called 'Standard' as well, but 'softcore' is the more common community term) mode and a Hardcore mode.
Dying in Softcore leagues is not terribly damaging. You suffer a penalty on your experience gains towards your next level, which can be moderately painful at high level, but your character otherwise goes on unscathed. Dying in Hardcore leagues, on the other hand, immediately removes your character from the league. Unlike many games (most notably the Diablo series) where Hardcore characters are dead forever, in PoE a dead Hardcore character is placed in the Permanent Standard league (even if you were playing a Challenge League on Hardcore).
Because your item stash is account-wide, dying on Hardcore does not move those items to Standard. However, any equipment your character was wearing is transferred along with anything in your character's actual inventory.
Playing on Hardcore provides no extra bonuses. It's simply for bragging rights (although it also tends to have a very different economy from non-Hardcore leagues).
Path of Exile also includes an optional mode called Solo-Self-Found ('SSF'), which is in effect a separate league. Solo-self-found disables partying and trading entirely: you must make all progress, in both combat and items, completely by yourself. SSF is, as a result, significantly more difficult, and items that are treasures by SSF standards might be purchased quite cheaply in non-SSF leagues.
Playing SSF provides no extra bonuses. It's simply for bragging rights.
In total, you can choose, generally speaking, between eight possible leagues:
- Standard, Non-SSF, Softcore
- Standard, SSF, Softcore
- Standard, Non-SSF, Hardcore
- Standard, SSF, Hardcore
- Challenge League, Non-SSF, Softcore (most people play this one)
- Challenge League, SSF, Softcore
- Challenge League, Non-SSF, Hardcore
- Challenge League, SSF, Hardcore
In addition to the long-term leagues listed above, there are sometimes special "Race" events available that last between a few minutes and a few weeks. These races usually have special rules totally separate from the main game rules: for example, every zone might contain special enemies, or drops might work differently, or it may even be possible to kill other players and take their equipment.
Most Race Leagues merge into Standard on completion. Some races that give excessively powerful or plentiful loot are "Voided", and are the only situation in which characters are effectively deleted at the end of a league.
Races are competitive, usually with the goal of reaching certain thresholds in the game's story as quickly as possible. As a new player, it's unlikely you'll be able to compete for top times, but completing certain objectives can still make you eligible for Microtransaction prize drawings (one of the few ways it is possible to get Microtransaction appearances without spending money).
Okay, So Which One Should I...
In general: play the Softcore, non-SSF, Challenge league. That's where most players are, and it's what most people who play the game enjoy. The only exception I'd recommend is if the league is about to end, or if you're in the gap between two leagues, in which case you might want to learn by experimenting in Standard first and then join the next league as it starts.
As of this writing (March 2019), this means playing the Synthesis league. This league started in early March 2019, so it should run until June or so.