League of Legends (LoL) Question: What would you suggest I get for my next champions?

Sounds like you are looking for a burst mage like Annie.

Not only does Annie have a very low price point, but she has a point and click ability, free stuns, and damage reduction (based on basic attacks).

Kayle is also great for mid lane as well. She has invulnerability with her ult, free heals, point and click, AND her main damage source comes from autos.

Just some ideas.

I suggest, you try and have a couple, perhaps 3 champions per lane. Try balance it out. I still, more often than not, run into players who get autofilled... cry the entire game and eventually lose. And it boils down to one thing - Don't play ranked until you have a few champs in each role which you can play safely... don't need to be a pro with that champ but if you start early you can still get a big pool of champions now and then master them slowly.

I would actually recommend Katarina as your next champ, or the one after the next. She has no skill-shots and is fairly mobile, so you you can dodge quite a lot. A few deaths aren't uncommon on her. If you're unsure who you want to buy, watch some gameplay from pros. This way I bought Ahri and later learned her.

try annie/ryze are low ip cost and relative easy to play, ryze have anyway skilshot on q but you can stun enemy before q.

or Vladimir but is 4800 ip, have no skillshots, have sustain, you can go ap or tank, or both and still do a lot of damage, your kit allow you to dive very safe and is fun as **** to play this champ after you learn how he work.
But he have a big counter, and this is called Grievous Wounds

Annie, is prolly the best pick for you. A mid lane champ which is easy to handle(not skill show reliant). Ahri is another option. She requires skill shot practice, but is generally not too hard and her skill kit is so abundant for options in any situation.
You say you are bad with skill-shot champs and tend to feed alot, which are feats to most mid lane and range champs, who are fragile and with complicated mechanics. Maybe, after all you should try with some tanky top champs and fighters. They wont require much skill shots and dont get bursted, but cant one shot either and require to be focused in longer battles and know how to trade until you win a lane(not necessary fight till death). Easy top champs can be Darius, Illaio, Sion, Garen, just in case you are curious to try

Lux is a very good start, she was my first mage and when you understand how to play her, which is easier than others (Ahri) then she can too very well, plus her price is low compared to others but Annie is always a safe pick.

Annie and Veigar are good examples of strong mages that are fun and easy to play!
I'd also highly suggest Malzahar, Heimerdinger and Lux.
These are very easy mages with a simple combo that you can learn and use in your games.
i hope you'll find your favorite mage champion ASAP so you can enjoy the game even more! <3