One of the reasons I ended up with the turbo tent was because I went cheap for my first tent. I bought a Wenzel brand, 8 person tent for something like $100.
It lasted all of 2 trips before the one of the poles broke, the zipper tore and something else I can't recall failed.
After the second trip it went straight into the trash at the camp ground.
I don't think you'll run into that problem at the price point you're looking at but do keep in mind that the large, cheap tents have to cut corners somewhere. Unfortunately that somewhere is likely the quality of the materials.
That said, if I was looking for a cheap tent something like this Wenzel might fit the bill for a season or two.
This is our tent, here, pretty massive, but I did that math and it fits into the allowed space with room to spare. I think you''ll be fine.
This is my car camping tent: http://www.amazon.com/Wenzel-Klondike-11-Feet-Eight-Person-Family/dp/B002PB2HPS/ref=sr_1_1?s=sporting-goods&ie=UTF8&qid=1425321885&sr=1-1&keywords=tents+wenzel+klondike
It's perfect for everything you mentioned.
I usually put the rainfly on and then just roll it back and use the attached ties to bundle it together so if the rain does roll in, two people can roll the fly down and you're completely waterproof in about 10 seconds.
I have had multiple friends stay in it with me that liked it so much they ended up getting the exact same tent.
I will say that the current amazon price is a little higher than what I paid, but that it's still worth it.
Only downside is that it's 27 pounds, so it's obviously a no go for any kind of camp site more than a mile or so from your car.
I just went through a kind of agonizing selection process involving screen room tents, and the rain issue just kept tripping me up. Very few tents "convert" on the screen room, as in they have zip-up windows and a floor - in the US I found the Wenzel Klondike 8 and the Ozark Trail 12p, which I think is actually a great option if mostly it'll be two adults but occasionally 3 or 4 adults.
I don't care about small footprint - we're mostly looking at campground and hipcamp camping the next 2 years, there's plenty of room, we use two enormous cots and need the space - but I wanted as much weather flexibility as I could get. I ended up with the Ozark Trail 8p Hexagon which I might end up regretting instead of getting the 12p above but I have had it up in my backyard guyed out like crazy while the Santa Anas blew and that potential issue, at least, can be dealt with. Neither tent is extremely promising in blowing rain, and I will probably rehearse some strategic tarping against the eventuality, but for decent weather and calm rain I think they're both solid options.
They're not going to be forever tents - Ozark Trail makes decent stuff but it's definitely not constructed like a $500 tent - but we wanted something we could also use as a literal day-use screen house just for chairs and tables and 4ish seated adults over the next two years and these fit that requirement.
I would actually buy sooner rather than later. I've been watching stuff go in and out of stock for a couple of months and I don't think it's going to improve any time soon.
I bought my sister this tent. They've loved it!
My first year, I brought this huge ass tent: http://www.amazon.com/Wenzel-Klondike-11-Feet-Eight-Person-Family/dp/B002PB2HPS/ref=sr_1_12?ie=UTF8&qid=1427737396&sr=8-12&keywords=tent
It was a tight squeeze, but it fit.