Below $150 is tough. In that range I would recommend a Coleman. I have one I have used for around 16 years so far, and it has been reliably waterproof. I still have yet to retreat it. I have an old 3 person tent. I used it for part of a bike tour in 2019 when my wife came to visit me, instead of my hammock. I ended up taking it with me when she left since I was going to run into some very bad weather, and though spending a day or so waiting out the storms would be nice in the bigger space. It was, and despite heavy rain and high winds, no water made it into the tent.
Here is a 4 person tent with a full fly from Coleman. I would recommend the full fly version from then rather than the shorter fly version.
https://www.rei.com/product/201634/c...-4-person-tent