If you can arrange 8'x8' for your rack then it will be plentiful for everything else

Edit: Please refer to my drawing,
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all values are pulled out from my butt, and i made a lot assumption but door's dimension should be quite standard around 900mm, which you can see if it is open inward you might have a bit problem.
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Those models i did not draw them but merely pulled from the trimble database and i scaled down the dimension for the treadmill as it seems a bit too large, this would be how i picture your homegym be like.

Edit edit:  TnY's suggestion seems more plausible
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