What permanent magnet motor is the best for the bike generator? How to decide about wattage?
I am aware that I will not be able to produce more than 100W anyway.


That's about right. Another useful number to remember is that a servant can give about 1 kWh per eight-hour shift!


  If I buy a motor with 24V 350W RPM2750 will I be able to run appliances which consume more power rather then I would purchase a motor 24V 250W RPM2750? 


There will be losses in any motor / generator and these will increase with size although they may be countered by improving efficiency. The 250 W unit will have lower inertia and will probably be cheaper.


  Does it mean that the motor with higher wattage will be more effective in running appliances which consume more power?


Yes, but as you've stated, your power source (you) is limited in output.


  As I understand, the adult person is able to run the bicycle with more or less RPM 60, so it means that in an hour I will be able to do RPM 360, ...


Umm, 60 RPM x 60 minutes = 3,600 revs/hour - but why are you converting to hours?


  which is 7 times smaller then RPM2750. 


Much worse than you imagine: \$ \frac {60~rpm}{2750~rpm} = 2\%\$ of rated speed giving you 2% of 24 V = 0.5 V out. This won't light an LED! The DC generator's output voltage will be proportional to rotational speed.



The article is too long for me to read but here are a few pointers:


You need to figure out what voltage your system requires.
You need to generate in excess of that voltage and regulate it. (It is also possible to generate a lower voltage and boost it with a boost regulator.)
If you go for 24 V out then you need to gear-up the motor drive to give 2750 RPM at your preferred cadence.
You need to figure out what you want to happen when you stop pedaling for a second or a minute. Do you want your cinema to reboot? If not you need some short-term storage.


I think a more practical project would be to power your cinema from a mains-powered battery and the bicycle generator. Monitor the generator output and if you fall below a certain threshold for a time then blank the video. If you maintain output for more than ten minutes then dispense a chocolate reward.