All good advice above. I'm going to weigh in from my personal experience, because your situation sounds much like mine a few years ago. I was 6'0", 375 pounds, but still pretty active and able to get around fine. But, I could feel myself slowing a lot and becoming much more sluggish. I wanted to start cycling, so with no research I walked into a local bike shop and bought a Trek 7.2FX and began commuting to work, 17 miles each way all on a bike path. I also changed my diet and began eating very healthy, but not necessarily cutting calories. I just replaced all the junk with healthy foods. The weight melted off, an I graduated to a road bike a few months later, and now, five years later, I am at 240 pounds and racing regularly, both road racing and cyclocross.
I share this story to give encouragement. Cycling has changed my life, and I like to share with anybody who is where I was. Don't worry about the looks, don't worry about what other people think. The bicycle shops will be more understanding than you might expect. I never once felt uncomfortable in a shop. They see it all the time, and they're glad to be helping with your weight loss journey and hopefully gaining a lifelong customer. I wore mountain bike cycling shorts from Aerotech Designs for the first year, then at about 325 pounds I started wearing lycra bib shorts. I joined a cycling club and just hung in there best I could until I got lighter and faster.
I highly recommend the Trek FX series for solid, entry level bicycles for us big guys.
You can do it, and it can be a life changer. Good luck.