Wow, that's a really big question. This forum is mostly about backpacking, which does cross over into running in some ways. e.g. - a lot of folks wear trail runners when they backpack of day hike.

I think to give any kind of ideas, we'd need to know what kind of running you're getting into. Are you road-running? trail-running? Are you training for an upcoming event? Do you have any conditions like previous injuries, narrow or wide feet? Are you just dipping your toe into running? returning to running after a hiatus?

It's kind of a, "What are you using this for?" kind of question we need answered before we can give you ideas.