By far your best bet is a used tent. Do your research first. There are quite a few used Tarptent Contrails around because a lot of "gotta have the latest tent" folks have bought the newer Tarptent Moment. However, I personally would pick the Contrail.
If you must have a new tent, the Six Moon Designs Skyscape Scout
is only $25 over your budget. It was designed for tall people!
Most tents under $100 new won't hold up and will leak. However, Coleman backpacking tents do pretty well (in my limited experience) and you might find one for $100 or less. Test with a hose in the back yard and seal the seams if they leak. Don't expect it to be lightweight. I used one in southern France once and it held up just fine through a violent thunderstorm followed by steady heavy rain that caused floods all over the region. Later on my son#1 used it in unrelenting rain in the Canadian Rockies. It weighed over 5 lbs. dry, though.
If you can't swing any of the above, this should be within your budget: 8' x 10' Equinox silnylon tarp from Campmor, $80
2 yards wedding veil material from local fabric store as bug net (drape from top of tarp)
Polycro plastic (for shrink-to-fit storm windows) from big box hardware as ground sheet
Mason's twine for guylines
Homemade stakes from metal coat hangers
Poles--either use your trekking poles or look at local outfitter
The total will be about 20 oz., making this probably the lightest as well as the cheapest solo shelter. With the 8' x 10' tarp, there will be enough room you can fit in a dog or possibly another person without too much trouble. Or you can use a cheaper (but considerably) heavier tarp.