whoop, your post wasn't showing so my response looks stupid. There are plenty of options you can take, but they vary in how you should play them. Zed is a great option that can fight a lot of mids and has high mobility and 1v1 capabilities. He is great at diving a team and eliminating squishies. There are some "magic assassins" as well. Akali has high mobility and can jump around in a fight as well as use her shroud to make fighting her difficult. However she is really only good at taking on one opponent at a time. Ahri doesn't have the single target burst like the other two, but has a strong CC move and more AOE team fight abilities. Fizz is also very mobile and is great at killing single targets, but has the benefit of his AOE ult.
There are also other champs that aren't exactly assassins, but are able to move around and deal a lot of damage. They are a bit more teamfight oriented, but also excel at killing single targets. Wukong, Fiora, and Master Yi all come to mind.
You honestly have a lot of options as for who you could main that can assassinate and deal tons of burst damage. I will tell you that glass cannon is not always the best way to go. You want to be able to survive some damage otherwise if the enemy team is smart, they will just kill you every time you dive in for a kill.