I've put all that you need to know in the notes next to the items you want to know more about.

Tristana has a combination of abilities that make her kit very useful for solo players. She can siege towers and burst enemy champions with her E. She can use her W to engage or escape enemies, and it resets on kill or assist, allowing you to hope around in team fights. And her ult gives you another option to escape, and combining her R and W lets you play almost like a Lee Sin, W'ing past an enemy and ulting them under your tower, or knocking an enemy back with your R and jumping right back on top of them.

She's a great option for solo players because her kit, as I mentioned, allows you to play more for yourself, you don't need to worry about your team to rush down towers, you have two options to escape and she has an easy engage with great burst damage.