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Nike Metcon or Free Metcon depending on if you're leaning more towards the squats or the running. Also kind of depends on your running technique because if you heel strike then you'd probably be better off with 2 different shoes.
Older metcons used to come with heel lifts in the box but my 7's didn't so if that's something you think you'll use try and find some 6's
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As dry says generally crossfit shoes are designed with this kind of thing in mind.
I'd say that chuck taylors or vans old skool are fine too. I prefer a heel when squatting now, but used to do all of my lifts in chucks, usually bought from tk maxxx for less than £20. No cushioning for the running side but that's not that big of an issue imo, esp for shorter distances.
Shoes. Is there such a thing as trainers that won't get squished when squatting but are also fine for a bit of treadmill running?