Bedrooms can be small while a lot of exercise equipment is massive or bulky. Because space is usually at a premium, it pays to plan your layout carefully. Your best bet is to measure the room to make sure you have enough space for everything. Pay attention to the door swing at the entry and any closets with swing-out doors. Make a note of where electrical outlets are located if some of your equipment has monitoring capability and will need to be plugged in.
If you don't have enough room for everything, make some tough choices now about what equipment you'll use daily, like an elliptical trainer or treadmill, and which pieces you won't mind taking out of a closet for occasional use. You can make a good start by leaving an area in the center of the room for floor work like Pilates and yoga, and positioning large equipment pieces around the perimeter away from doors and heat registers. If you do occasionally set up additional equipment, it'll be easier to move it into the central space temporarily. Give yourself at least 28 inches between the outermost projection of a piece of equipment (including you using it) and the nearest solid object, like a wall. More space is definitely better.
Unless the bedroom you have in mind is the size of an auditorium, you'll probably have to lose some of your wish-list items, like the comfy, overstuffed chair, but don't lose all the amenities. Exercising can be a tough, boring slog without some incentive, and including sound and video equipment in your design -- and maybe a mini-fridge for water and the occasional juice beverage, could mean the difference between doing the requisite number of crunches and heading to the kitchen for a leftover slice of pizza, instead.
To conserve space but still provide room for little stuff like exercise videos and games, install shallow wall shelving and other wall mounted options. We like the idea of a swing arm mounted flat screen because it can be positioned for viewing from anywhere in the room. Exercise is about getting the movements right and being consistent, but the more comfortable and convenient you make your workout, the more likely you are to stick with it long term.