Most importantly, your colleague needs to learn that weight reduction will come about through changing their diet. While exercise will help, it contributes to general health and blood pressure reduction far more than it does to weight loss.
This is a great time to point out that this site is not a medical resource, and your colleague should see a physician before undertaking any serious weight-loss program.
What kind of ride would be best?
That depends on where the bike will be ridden.
What kind of routine would give the best result?
What time is most suitable to go for such ride?
As Daniel has pointed out, the best routine is one that will be followed. A good rule of thumb is a minimum of half an hour three times a week, but more would be better.
Motivation is extremely important here. Is this person someone who functions better with a structured program? Then a series of scheduled rides may be best, putting aside certain days of the week as "workout days". Is this someone who has trouble staying motivated for long-term goals? Commuting may be the answer, working the rides into their daily routine. Perhaps utility cycling would be best? (That's where you run errands, go grocery shopping, and so on, all on your bike.)
Exercising in the morning can be beneficial for some, but others find the evening to be best. Experiment until a sustainable routine is reached.
What should the diet consists?
What are the re-hydration choices during/after the ride?
Personally, I prefer regular food and water. However, some riders - mostly roadies - prefer sports drinks and gels for their nutritional needs during the ride.
A good rule of thumb is to have protein before a ride and dairy or carbs after. But experimentation, again, will help here. This assumes that there are no specific medical complications.
How to control the fatigue level to control the stress level?
How to make it a more enjoyable experience?
Eat properly before a ride, don't push yourself too hard at first. Working out should tire you but not exhaust you.
What kind of bike is the best choices?
How expensive should he go?
Your first bike is always a bit of a guess: You don't know what kind of riding you'll be doing until you do some riding.
Hybrids and hardtail mountain bikes are usually a safe bet. It's worth pointing out that road bikes and folding bikes often have weight limits and can be unsuitable for riders that are extremely heavy. These bikes are extremely flexible and will handle a variety of terrains.
I'd avoid carbon road bikes or mountain bikes with disc brakes or full suspension; both of these types almost certainly garbage when you get a budget version. However, an entry-level hybrid or even a comfort bike in this range will serve a rider well for some time, and can be pressed into service later on as a neighborhood bike or utility bike.
Just be aware that some people start riding but it doesn't stick. There's no shame in that, cycling isn't for everyone.
The best thing you can do is to be supportive: Tell them about fun places to ride, offer to go along for short day rides. Maybe you could suggest they go on a group ride later on.
But I'd hold of on pushing a century or a week-long tour on them until it's clear that they enjoy cycling and won't be giving up the new hobby anytime soon. (More on that in this answer.)
