Welcome to the club!! I used to ride upwards of 300 miles per week and did some racing and time trials but work, lack of time etc etc in the last 8 years or so has nearly done me in.
I cycle road and mountain bikes and there's no reason you can't whatever weight you are, you just have to make some allowances for your extra weight.
Firstly, for road cycling, don't waste money on all the uber-lightweight bikes and wheels they'll do you no good and a lot of carbon frames carry a weight limit. Gearing, at least have compact chainset but better triple front chainset to give you lower, easier to pedal gears.
Keep your targets small to start with until you build up some aerobic capacity, if you have somewhere flat to go locally, use that until you start losing a bit of weight before you tackle hills, and when you do start on hills take then steady. Mountain bikes are most suitable but murder on the road and it's very difficult to find offroad areas that don't have hilly bits in them.
If, like me, you're metabolism is shot to hell you'll need to watch what you take in because you will not be able to sustain the energy levels you need without things like the odd energy gel and proper energy drinks. You will not be able to metabolise the glycogen stores you have quickly enough to complete even short distances without struggling to cope with the energy demands.
Clothing can be an issue Prendas.co.uk do a lot of larger sizes, it's important you at least have a decent pair of shorts with a proper chamois pad otherwise you can cause a lot of damage to your nether regions blistering is not something you want down there!!
Stick at it though, I was 22 stone when I started riding again in August last year, dropped 4st, my blood pressure is almost normal and i can almost breathe properly again, I'm still working on my metabolism and it's getting better. I've done a couple of 100km rides on the road and have started cracking some good hills. Unfortunately much of the work ive done in the last two months has been on a turbo trainer because of the poor weather we've had, safety first is important, you don't get much grip from 23mm slicks on frosty icy roads, and as for the winds we've had....
Keep at it, it does a make a massive difference, good luck