I'm about 5'11", but I was 270 lbs when I started riding (down from 300 lbs).
I bought a $225 Giant Cypress ST (the low-end steel, heavy thing). I first had problems with wheels (spokes breaking). I eventually paid to have to nice strong wheels built by a local wheelbuilder (cost more than I paid for the bike). I beat the crap out of that bike.
I rode many thousands of miles on that bike before retiring it. I had cracked the bottom bracket shell (part of the frame). I kept some of the nicer parts I had upgraded to move to my daughter's bike (another Cypress ST).
I've moved on, and I have four nicer bikes now, but if I hadn't started with that cheap bike, I wouldn't be where I am now.
My daughter's bike is still going strong. I recently added a hand-built front wheel with dyno-hub for lighting. She's 19, car-free, and an athena. That bike is her freedom.