I have a bike and a training stand (or whatever you call those things you connect to your back wheel to convert your bicycle to a stationary one) that I use for exercise. However, it’s a hybrid mountain bike, and the handlebars are so low that I have recently gotten back pains after prolonged use.
I used to have a treadmill. It was okay, but I find elliptical allows me to exercise longer and a higher pace with less wear and tear on the knees. Just one man’s opinion.
I would go for a trial membership at a gym and try all the equipment out before making a decision. And maybe consider a rowing machine.
But don’t expect to be able to lose much weight through exercise: it takes a lot of time and effort to burn calories through exercise and no time at all to eat them back.
I don’t think there is one best answer. It depends on you. I have great luck with a dedicated exercise bike. My girlfriend vastly prefers a treadmill. If you get the one that suits you best, you will get much more exercise on it.
I recommend you buy a one-month gym membership and give them each several tries; maybe a week on each one. By that time, you’ll know what “feels” right to you and your body.
I’d go with the elliptical. The whole idea behind these is to raise your heart rate to a set level for a good 20-30 minutes in the most comfortable way possible.
I don’t find bike seats comfortable enough to pump away on for that amount of time and treadmills, while being my second choice, aren’t as nice on the joints as an elliptical.
Swimming would be my first choice but that’s not always convenient.
Personally out of the three I prefer the treadmill as it has the potential to make you work the hardest - although if you have trouble with your joints you might want to bin it as it can really wallop your ankles and knees. You don’t want to buy one and then realise it’s not for you, so I second the notion of a gym membership to see which you like the best.
If that’s the only issue with your current setup, it’s easy to raise the handlebar by replacing the stem, or changing to a curved handlebar (here’s an extreme example).
I really like the elliptical. But if you look around my gym, it would seem that all 3 of your choices are equally as popular for a variety of body types.
It’s not quite clear from your description, but do you have the front wheel propped-up on anything? Before trying a bunch of different things, if this set-up has otherwise worked for you, try placing a couple of pieces of wood, maybe 2x4s stacked under the front wheel to raise the handlebars. See if that helps with your back. They also sell wheel-rests for this specific purpose (example).
It depends on where you are and what you enjoy doing. I live in New England, and I’m certainly not going to be riding my bike outside in January. I have a bum knee, so much as I used to like running, it won’t be happening again. I don’t like treadmills anyway.
I personally like an indoor bike, with outdoor walks during nice weather. YMMV.