Probably this has already been covered but I don't have time to read all the posts, so here is my (repeat?) advice.
You need to go see a heart doctor and get a complete heart checkup before you tough it out. A regular physical will not be sufficient. Please get a complete workup. I say that because I had a friend who was 48 years old, when in to get a physical because he wanted to start going to the gym after 20-some-odds years of no exercise, the doc ok'd him, so he went to the gym one morning, went to work and died at his desk from a heart attack.
There were two things my friend didn't do that led to his death.
One was that he didn't go to a heart specialist for a complete workup; and two, he started out doing too much too soon.
So, if the doc says you're good to go, take it easy for about 3 months, slowly workup up the miles, don't go pounding the pedals, just ride at an easy pace, and don't see how far you can go, take short rides of 2 miles and slowly, once a week, add about 10% more miles. Even if you ride that first 2-mile ride and your like, "man that fool doesn't know what he's talking about, 2 miles was easy, I'm going for 15." Not a good idea, your blood and your heart have to slowly get stronger and the blood has to slowly get thinner, it takes time for that stuff to get used to what you are demanding of it.
Don't let your ego kill you, take it slow.
There are Century training schedules on the internet too, once you get your 3 months of riding in and you want to someday do a 100-mile, or even just a 50-mile ride, if you follow a schedule, you can do it, but the key is to follow it by the letter; but don't start such a schedule till you do those first easy 3 months of riding, and don't speed up the schedule or you could hurt yourself.
Riding a bike consistently, like running or going to the gym daily, takes a lot of mental discipline, discipline that most people don't have, they'll start an exercise routine and quit within 3 months due to all sorts of excuses. With that thought, do not go out and buy an expensive bike, start out with a good mid-end used bike around the $350 range or lower, then if after a couple of years of consistent riding then you'll know that you're mentally ready for a better bike. The last thing you want is to spend $800 or more on a new bike only to have it turn into garage art in 3 months to a year.