What will you enjoy doing inside?
I hate to ride a bike on a trainer - I'd probably use an elliptical machine more (if I'm riding, I want to be outside). LBTC is right - if you used it enough to burn it out, you might want to get another
Ellipticals do a nice job on arms and indirectly help abs some. I think you can get a better ab/shoulder workout in other ways (e.g. weights and a balance ball) than a rowing machine. I'm not a big fan of using those either (I can do other things for longer/higher intensity, so I burn more calories).
So...think about what you want to do for exercise and when you want to do it. If you think you'd go to a gym, join one. If you jump on the machine in the house when you really don't want to face the world (ahem - I do that), then get something for your house.
CA
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