Just my 2 cents. You can also try suspension training, such as the TRX. I am not saying you need to spend a ton of money on any one system but suspension training has some advantages for a person with limited space.
The trainers are very small, portable and can be fixed to just about anything. Most have door anchors and straps to wrap around beams, bars, poles, etc.
It is very scalable; just change the angle of the exercise, or alter the number of reps, rest interval, etc.
It is very adaptable; you can focus on cardio, strength, flexibility, and balance. It always works your core and you can choose a variety of exercises and routines to achieve your goals.
You can look up videos on you tube for various workout
routines or just buy a system that comes with videos.
Anyway, given limited space, Suspension Training is another option.
You can also do tons of calisthenic exercises in a small space. See the Guard MC Train Up on the home page for some ideas.
My recommendation for a good diet
is "The Zone". Google it and buy the book