First off, League of Legends is free. That means FREE, every character is unlockable through points you earn in-game. Of course you can just pay for them, but since acquiring new characters to play as is kind of the metagame that ties each session of League together, that spoils your fun. You DO need to shell out money to buy alternate skins for your toons, but not having those won't hurt your enjoyment of the game any. Buying the retail box gets you some unlocked characters and free skins off the bat, as well as credit to buy more, but now that it's a semi-rare product it isn't worth the prices sellers are asking. I wouldn't buy it used either; since all the unlocks are probably already claimed.
Now to the game. League of Legends is a standalone successor to the Warcraft 3 mod Defense of the Ancients- essentially an arena deathmatch action RPG. Think Dawn of War 2 without the units, or for us oldsters, Nox multiplayer (that alone should get you interested). Players choose an avatar with unique abilities then head out to one of 3 unique killing fields to assault capture-able points, destroy enemy towers, fight streams of minions, and assassinate enemy players. Throughout the battle your hero will level up gaining new abilities; you can also buy them equipment to further customize how they play. This all resets after every fight, but winning increases your "summoner" level, and allows you to buy new champions and persistent upgrades that you take into each fight. Combat is hectic and fun, and the short match times of LoL (about an hour at the most for a tense match on the largest map) help keep frustration low.
Graphically League of Legends is about on par with World of Warcraft- the devs wanted people with lower spec machines to be able to enjoy it, so they went with a cartoony look instead of realism. Environments are well detailed though, and champions look very sharp and appealing. Sound is well composed but forgettable. The quality of the voice-work varies depending on who you pick.
League IS multiplayer only, which leads to certain constraints. You must work with your team to succeed, and your game can (and will) be ruined when teammates decide to not pull their weight. Dropping from a match, even by accident is penalized, eventually through temporary bans. Matchmaking is blind, so you either play a planned game with friends, or a blind one with strangers (there is no "match from my friends" list option). You will be kicked from a match if you idle too long and if you do not rejoin before the end, again, penalties. All that said, LoL has the friendliest player base of any game I've ever played online, and most folks are there to have fun. And while Riot's sportsmanship policies are a little draconian, they also hand out a lot of freebies to loyal players. And can you fault them for trying to keep their player base honest?
Bottom line is that League of Legends is a decent looking, fun multiplier game that recalls some of the best aspects of classic strategy and ARPG games, and has a huge, thriving player base to play with.