Putting new tires on my '08 yaris soon... what do I need to know?

[hannahyaris]

I recently bought my first car I have a 2008 yaris base sedan
aaaand now I need to buy tires.. What do I need to keep in mind while I'm looking?

I think the size is P175/65R14.
My budget is under $400. I would like something that handles well on wet and dry roads.
I tried viewing the official wheel and tire guide but it was like a foreign language to me. Please excuse me, I'm pretty new at this.

Thanks!