Looking to buy a bicycle for exercising and recreational activities, that will fit in a car
First off you will need to have a think about what kind of riding you want to do. For roads you'll want a touring bike, and for off road, a mountain bike. The key differences are:


Weight - riding rough trails and off road requires a strong frame. This will impact weight
Suspension - again, this adds weight, but can be essential on really rough terrain
Wheels and tyres - on the road smooth tyres require less effort, but off road you need grip


Then you'll want to find a good local bike shop (LBS) and ask about sizes. They will be able to advise on frame length, handlebars, seat type etc to suit you. 

EDIT as mentioned below - get a helmet!

For fitting in a car, as long as you can remove wheels (these days you can get all types of wheels with quick release mechanisms) you should be able to fit them. In a saloon car you may need to be able to drop back back seats.

At begineer level, you really don't need to think about much else as far as the bike is concerned, however you will want to get lights, a bike lock and other accessories such as a speedometer (maybe gps), water bottle, and also things like cycling gloves (your fingers can get very cold on a long ride) and cycling shorts (again, for a long ride, the padding can be very important!)