I just want to know if these particular Champions are effective or not. I picked these ones based on their lore, appearance and play style. I know nothing about their effectiveness when played properly as I'm only level 11 and also quite new to this game.

Aside from Garen and Jayce I currently have none of these Champions. Also each link leads to their respective Champion on the League of Legends Wiki.

Garen, the Might of Demacia
Lux, the Lady of Luminosity
Jarvan IV, the Exemplar of Demacia
Caitlyn, the Sheriff of Piltover
Jayce, the Defender of Tomorrow
Vi, the Piltover Enforcer
Ezreal, the Prodigal Explorer
Irelia, the Will of the Blades
Master Yi, the Wuju Bladesman
Riven, the Exile
Taric, The Gem Knight
Kayle, the Judicator
Lee Sin, the Blind Monk
Ahri, the Nine-Tailed Fox
Pantheon, the Artisan of War
Fiora, the Grand Duelist
Shen, Eye of Twilight
Leona, the Radiant Dawn
Tyrndamere, the Barbarian King
Ashe, the Frost Archer

Of course I don't expect one person to have all the answers but I would like to get at least one answer per Champion. Thanks a lot in advance.

Quick edit: I also forgot. Sometimes my internet connection decides does it has to disconnect mid game and while I make it a point to come back quickly this seems to have gotten me a "Level 1 Leaver Warning" is there a way to decrease this?

Lee Sin is OP.

FreeLO.

Yes to all, though of course they are effective in their different roles, not all in the same role. Some are also more niche picks than others, for example Fiora.

As for your leaver warning...it's based on % games played that you left, and while reconnecting does help, it doesn't completely nullify the fact that you left to begin with. Play more games without leaving, it'll go down. Otherwise, consider fixing your internet.

Garen, the Might of Demacia
- Very simple, a very good "My First Top" champion since he hasn't mana or energy to worry about.

Lux, the Lady of Luminosity
- A very good AP Mid champion, but you gotta hit those skill shots so she's not the easiest to master. Can also be used as a support AP so that's nice!

Jarvan IV, the Exemplar of Demacia
- Good jungler, good top... can be used if you're willing to go against the meta as a AD Mid to ruin someone's day and is also an infamous "Kill Lane" support.

Caitlyn, the Sheriff of Piltover
-Strong early/mid game, weak late game. Good beginner champ cause she has a nice escape/wall jump ability, the highest non late game Tris/steroided Kog attack range, and can trap routes to her lane and control brush if her support is a slacker.

Jayce, the Defender of Tomorrow
- One of the "Big Four" tops. Is slightly countered by Irelia, counters another "Big Four" Darius, and then goes even or beats anyone else.

Vi, the Piltover Enforcer
- Don't know much about her, cept she seems like a pretty good jungler and if she does well, your ADC needs to watch his ass cause she's coming at him fast and hard.

Ezreal, the Prodigal Explorer
- Good poker, has great escaping ability. Not much for a late game unless the other team doesn't have champs to stick on him and kill him.

Irelia, the Will of the Blades
- One of the "Big Four" tops. Forget whether it's Darius or Jax who counters her...

Master Yi, the Wuju Bladesman
- Can be used in competitive play against the right team. Otherwise, Melee Carries like him have a tough time but are notorious "Noob Stomper" champs cause they can get out of control.

Riven, the Exile
- Great champ for top lane, might still be a good jungle. Much harder to use than you would at first think... definitely not a female Garen.

Taric, The Gem Knight
- Very good support, scary with certain dangerous early game ADCs.

Kayle, the Judicator
- Can be played as AP Mid, AD Top, Support, Jungler, ranged ADC, or Hybrid any of the above. Very versatile champ that can get outta control late game.

Lee Sin, the Blind Monk
- High skill cap top or jungler, OP once upon a time but people started taking him mid to beat up on AP squishies... so he's gonna be nerfed to oblivion. I'll miss you Lee...

Ahri, the Nine-Tailed Fox
- Fun AP Assassin!

Pantheon, the Artisan of War
- An okay top in some matchups... or a deadly hard counter to AP mids if you can have someone else on your team take up the AP damage duties you'd be lacking with that comp.

Fiora, the Grand Duelist
Melee Carry. See Master Yi... cept more viable.

Shen, Eye of Twilight
- Always banned and I don't play blind pick. Haven't seen one in 200 games or so...

Leona, the Radiant Dawn
- Most fun support in the game. Unless you're losing your lane, then the least fun support to be playing. She all ins the enemy and hopes you kill them and not the other way around.

Tyrndamere, the Barbarian King
- Melee Carry. See Master Yi and Fiora. Viability somewhere in between maybe?

Ashe, the Frost Archer
- Unique ADC since she can initiate with her ultimate which kinda helps you be more flexible with your team comps.

Garen, the Might of Demacia - great champion for beginers, high health, damage, easy to play with and no mana
Lux, the Lady of Luminosity - A good mid, annoying ult, can be played as a support but I dont think she is a very effective support
Caitlyn, the Sheriff of Piltover - my third favourite ad carry after teemo then corki, great champion
Vi, the Piltover Enforcer - quite hard to start with, really good at burtying people down, great jungler and solo top
Irelia, the Will of the Blades - a lot consider her to be OP, personaly I have only played her once and didnt really like her
Master Yi, the Wuju Bladesman - good champion, really powerful when fed, effective both AP and AD, just spam alpha strike and you can't go wrong!
Fiora, the Grand Duelist - A lot of people consider her to be OP, really good champion
Tyrndamere, the Barbarian King - Don't really like this champion personally but a lot of people do
Ashe, the Frost Archer - Not my favourite mid, in my opinion a ok champion

The champions I missed of I haven't played as much or dont really have anything to say about them

wow that's a really long list... I'll just comment on the ones I play:

Caitlyn, the Sheriff of Piltover - Good ADC, very strong in lane because of her long range but one of the weaker ones late game because her damage steroid isn't really that great.

Jayce, the Defender of Tomorrow - I've seen him played Top, Mid, ADC, or support. He's best top IMO because he matches up pretty will against most other tops and he can make good use of his mobility there.

Riven, the Exile - Played Top, Jungle or sometimes mid. She stronger in the S3 jungle than she was in S2 but I still think she's best top where she has room to make the best use of her mobility.

Taric, The Gem Knight - Excellent support, he goes well with almost any ADC and he does a little bit of everything, heal, buff, and cc. His only downside is that he only has one ranged attack that's kind of on a long cooldown and sometimes he's not the best pick because you need a support who's more specialized.

Kayle, the Judicator - Very versitile champ who can play any role decently. I feel like she's best either top or support. Top lane she just bullies people away from minions with her harass and as a support being able to make your adc immune to damage is pretty sweet. Downsides would be that she doesn't have any hard cc and it's hard for her to do damage later in the game when she's on the limited budget of a jungler or support.

Fiora, the Grand Duelist - Fiora is a melee adc, she's one of those champs who can really take over a game if she gets out of hand. She's usually played top but she can also jungle and I've also seen her played bot lane in place of the adc or in mid. The problem with Fiora that she has no cc and there's certain champs that will just really shut her down in lane so she'll be under farmed at the end of the laning phase if she has a bad matchup. This is the main reason you don't see her played more, she kind of an unsafe pick overall.

Leona, the Radiant Dawn - Leona is another really great support champ. She started getting a lot more popular after recent nerf to healing supports. Leona is an aggressive support with a lot of cc so she is best paired with adcs who can take advantage of this like graves, corki or ezreal. Downside is that she doesn't have any sustain and if she's paired with a more passive ADC like Ashe or Cait she isn't really that useful.

Ashe, the Frost Archer - Another good ADC she's kind of middle of the road in terms of power throughout the game. She's pretty passive during the laning phase because it's really hard for her to kill anybody without her ult. The big thing she has going for her is her utility. She can keep somebody slowed permenantly with her Q and if you can land her ult on somebody squishy it's bad news bears for them.

Awesome info guys thanks.I'm gonna get these Champions and I'm glad to know that they're all useful.