Ok, so I checked and supposedly you are level 7, so you are just getting into League. And when I check out your game results on na.op.gg that is somewhat supported as it shows only 18 games total.
That said, there are a number of things I might say. I'll try to give you the best advice can think of
First, each week try out several of the free week champions. You can start with a Co-op v AI match, or you can see what you end up with in ARAM, but the key is to test out champions. You will probably struggle. You will make mistakes. You might have some smurfs get on your case for poor play, but you'll also learn how each champ works and more about when and how to use different abilities.
Second, you've played so few games that its hard to say "get X champ." What I can do is give you a bit of a breakdown of champ types and where they play. At first its good to choose 1 or 2 roles to practice/learn first and you should concentrate on mostly getting champs who are playable in that position.
So breakdown by type
ADC - ranged, usually have weak early, but very strong late games. Can sometimes be played mid or top, but the majority only do well bot lane with a support. You have 2 in Ashe and Tristana and I saw you played Jinx. There are differences in them based on ability sets. Ashe, Jinx, Kogmaw and Varus are well known for low mobility but surprisingly good utility or CC. Tristana, Graves, Corki, Vayne are known for higher mobility, but trade away some CC in exchange for the ability that gives them mobility. Playing an ADC is often a personal choice based on play style. Some are "lane bullies", others are better for passive farming until the laning phase is over You kind of need to try each one and decide which ones feel right.
Tank - Melee, with good defense and usually some good CC. Depending on their skillset they can be played just about anywhere, but some are better in specific roles. Garen is best in the top lane although he can be played mid against some team comps. Alistar is very good in the support role, but people have taken him jungling. At your level you don't want to try jungling. (you really need level 10 for smite and level 20 for tier 3 runes). Again this is a matter of personal preference, but you do have the 2 best beginner tanks already.
Bruiser - Melee, but usually build more damage items than a tank. Often have strong skills for fighting 1v1. I saw someone name Tryndamere and Aatrox who are both good bruisers. You see them jungling and top lane with rare appearances mid. If you enjoy melee fighting these can be fun to play.
Mage - Mostly shorter ranged than an ADC and do much of their damage with abilities where an ADC can do the majority of their damage with auto attacks. Mostly played mid, but some appear top or support and a few can jungle. Sona played mid would be considered a mage. Annie would be a better choice for a beginner.
Assassin - Melee, but designed around abilities that allow them to kills champions in one burst of damage. Most take time to learn to play to their potential. Most also play in the mid lane so they can roam since they need to get kills to keep up with champions who can kill minions quickly. They've fallen out of favor in the current meta.
Support - Basically a champ that has some mix of crowd control, healing and protection. They will travel to the bot lane with the ADC and their role early is to keep the ADC alive and try to help the ADC kill the other teams champions. It's not a popular role to play as you don't get gold quickly and are expected to do things like ward. Sona is almost always played in this role. She's very good at it once you learn which items to buy and what skills to level when.
So I'd say find a type you like and a role/lane to play and look at testing out any champ that might fit there.
Next, at your level you'll make mistakes. Try not to take them too personally, but if someone calmly gives you advice listen. They might help you uncover mistakes you can correct.
I'm willing to help if you run into me in game. I'm not great at mid or top. (my reflexes are too poor for me to beat most players and I'm out of practice), but I can definitely help you with Sona, Ashe and Tristana. I also might be able to find others to join in so you can play in a bit more relaxed atmosphere as the groups I run with try to be very nice to new players.
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I will say if you like Sona you can definitely get her when you can. Riot does allow you to say "oops, I don't think this champ works for me" 3 times, so if she really doesn't work out you can get a refund, but she has the advantage of being a solid champion with a skill set that it not too complex for a beginning player. At the same time learning where to position her and when to use each skill takes time, so you'll develop some strong play skills that can be used on other champions.
See you on the rift.
Possible Champion: Sona
