Wiring electrical outlets from a single outlet
The best solution here, would be to find a UL approved device that can satisfy your needs. Building your own device can be risky, and fraught with unexpected dangers. There are tons of UL approved power strips available on the market, it hard to imagine you wouldn't be able to find one that suits your needs.
If you must build your own solution, you'll want to be aware of at least a few of the dangers.
Exposed wiring
First and foremost, you'll want to make sure nobody can ever touch anything that could be energized. This means that all connections, splices, junction, etc. should be contained within an enclosure. You'll also want to make sure the enclosure is listed for the use, so that it will also contain any sparks, heat, etc. that might be produced.
Most areas now require tamper resistant receptacles in living spaces (living rooms, bedrooms, dining rooms, etc.), so you'll likely want to use TR receptacles for this project.
Overcurrent
While there are no hard-and-fast limits on the number of receptacles on a circuit, or the number of devices that can be fed by a receptacle. You'll want to be cautious not to overload your wiring. In industrial and commercial settings, 180 Volt-Amperes is the value that's used to calculate receptacle loads.  If you use this as a guide, you should have no problems with overloading the circuit.
While the circuit breaker should protect the house wiring, you may want to protect the wiring in your cabinet from overload as well. You can do this with a fuse, or circuit breaker. You'll want to wire this in as the first device, possibly putting it in the same enclosure as the watt meter.
Surge protection
Since you'll be dealing with expensive electronics, you'll probably want some form of surge protection. There are receptacles available that offer surge protection built in, but they may not offer the level of protection you require, or that can be found in a manufactured surge strip.