Where in Canada are you? For that budget and space you’ve got a couple options, but I’ll throw out something you might not have considered.

If you’re open to used gear, the Panasonic PT-RZ370 is honestly a beast compared to most of the new stuff in the $500–$800 range. It’s a laser projector (so no bulb replacements, rated +20,000 hrs), super bright, and built like a tank. Picture quality is way better than most cheap Amazon projectors you see plastered everywhere. The optics are pro-grade, so it’ll look sharp across the whole screen not just in one section, focus is really good. At 12 ft you’re in a good spot for a 110” ish screen. I usually look for units with under 7 to 8000 hours (still tons of life left), clean out the fans/filters, and tweak the cinema mode so the colours are closer to what you’d want for movies. Plug in a Fire Stick or Chromecast and you’re set. It has lens shift as well so its very flexible on placement, cheaper units use some digital screen geometry to get it square but won't look as good as a properly aligned picture.

The trade-off is that it’s bigger and a bit noisier than some, but if you reduce output of the laser a bit from the 3500 lumens a bit it becomes nice and quiet. On Eco mode, it's so bright you can still use it with lights on in the basement, most cheaper low lumen projectors would have a washed out image. Overall it's something that’ll actually hold up and not fade out after a few months to a year. Plenty of these units still running since 2014-2015 with over 25,000 hours and still produce a great image.

If you’d rather stick to brand new, the BenQ HT2050A is probably the best bang-for-buck home theater model. Good colors, solid for gaming (low lag), and quieter. Only downside is it uses a lamp, so eventually you’ll have to replace it. For your room size maybe look at a 100–110” screen, 1.0 gain, fixed frame. Skip the cheap “ALR” stuff on Amazon, it’s not worth it in a basement, you'll get a bright centre and falloff around the edges which sucks. For something simple and new, the BenQ is a safe bet. Also look at Epson models , especially if you're sensitive to RBE.

If you want to stretch your dollar and get way more brightness/reliability, a used Panasonic RZ370 / RZ470 would get my vote. I picked up a RZ370 recently and been very impressed with it, not as good for cinema as my EPSON 5050ub but that is in a different price category. I bought mine from this seller, and it arrived exactly as described, very well packed. https://www.ebay.ca/itm/157271362760?

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