I wear glasses and when I have my sunglasses made, I always have polarized lenses.
They reduce the glare from the sun….a good example is when you are driving and you get a sun spot reflecting off of a car's rear windshield, it is greatly reduced.
Oddly, when I have looked at a pond/pool of water, I can see right through the water where others only see the reflection of the landscape from the water.
Is it critical to have?
I don't think so, but I think it is worth it enough to pay a few extra bucks for it on my lenses.
More important is that you have UV protection on the lenses, which should be standard.
As for tents….you said no tarps.
How about a Henry Shire Tarptent?
I have a the one person Contrail and buddy has the 2 person Squal 2.
Think that the Squal 2 should fit your budget and it is about 2 lbs.
Hope that helps.