Firstly Chris, welcome to the forum!
There are three aspects to losing weight. Right mindset (this is the one that is neglected and yet it is the most important), healthy eating (good food in proper portion size) and smart exercise. It is about exercise that you have asked so I'll deal with that in this post.
My first guiding principle for myself was "to do no harm". If I exercised and ended up in hospital I wasn't going to do myself any favours. I went to the doctor to get a general health check and a management plan for my asthma which was out of control at the time. This was done before I did anything else. The principle of "do no harm" is about listening to your body. It will tell you what is wise or not. For me I had to consider where I was starting from. I had a belly hernia the size of my fist so that ruled out any exercise that involved lifting weights, sit ups or push ups or the like. The good thing about people of our weight is that because we are hefting so much weight around generally our leg muscles are in great condition. So all my exercise is/was based on what my legs can do.
I started simply with a 10 minute walk each day (I started in my second week - ever the reluctant exerciser). That was all I could manage before my back gave me too much pain. Each day I would increase the distance and/or speed and time. I slowly built that up to an hour walk which I managed to reduce to about fifty minutes by upping my speed as fitness occurred. I slow converted my walk into a jog when walking became too comfortable. Using lamp posts as markers I would jog one length between two posts and then walk until I was ready to try another length. I would do that at the second part of my walk. Then one day I just jogged the second part of the circuit. Very quickly after that I was jogging the whole circuit. Then I increased the length of the circuit so that I would be jogging for an hour.
Swimming played a major part in my exercise. I would go for an hour at least three or four times a week (sometimes daily). Water supports our weight and gives relief to our overworked backs. When I started I would do as many laps as I could (usually breaststroke). When that got too tiring I would walk laps in the pool making sure that I resisted the water with my hands. When my swimming got stronger I would just do laps alternating between breatstroke (6 laps) and breaststroke without using the feet (6 laps). This developed my arm and back muscles. I would try to do as many laps in the hour as I could. The trap with the pool is to avoid sitting in the water and chatting to the other people who are trying to lose weight but are not. This is not a social occasion...you are there to lose weight.
The exercise bike is really effective but not for the faint harded. When I started I did five minutes and thought I was doing well. You really want any exercise that you do to last at least 20 minutes. Don't worry about speed at first...the length counts more when you start. I use to do a "Four minute workout". This was basically a warm up cycle of 5-10 minutes followed by four lots of 40 seconds as fast as you can and then recovery cycle of 20 seconds, after that a warm down cycle of 5-10 minutes. Nowadays I do 30 minutes three times (burning about 1,500 cals.) at top speed with third level resistance...that will maintain my weight for the day without any other exercise.
My daily weight loss routine was varied. One moderate day, followed by a hard day with an "easier" day for recovery. Always challenge yourself to do more. Push hard but never break yourself.
That's it in a nut shell. Any questions?