Requirements

If no sunrise LED is needed, then the electronics could be powered from a 5W USB wall charger.  The sunrise LED will probably need about an extra 10W.

Cable

Not all USB cables are made equal.  I read about it in the past and I ran into the same problem.  The cable I originally used, had an AWG28 for power.  I lost more than 1V over it when the light of the circuit was on.  Only 3.13V remained at the 5V signal (the power supply also has internal resistance).  This resulted in unstable behavior with the MP3 player.
Switching it with a AWG24 cable, which had a much lower internal resistance fixed my problem.  USB Cables of AWG22 and AWG20 also exist, but these tend to be longer or much more expensive.

Backup

The common solution is to use a goldcap as back up power supply.  The limitations of goldcaps are:

• limited energy storage capacity
• high internal resistance
• voltage decreases linearly with respect to the current being drawn.

All of this makes that in case of power outage the goldcap can't be used to sound the alarm to wake the user.

An alternative approach will be used here.  A cheap alkaline AA-cell will power a MCP1640 boost converter that will step up the voltage to the required 3V3.  As long as the normal power is supplied, the MCP1640 can be disconnected from the AA-cell.

Filtering

DCF-communication is susceptible to noise.  Proper filtering is needed to reduce the risk of bad signal reception.

• ANP002: The Protection of USB 2.0 Applications
• AliExpress 32707561851 : USB EMI filter
• USB Hardware Design Guidelines for FTDI ICs

Connector

USB-C connector

USB-C allows for a maximum power transfer of 20V/5A.  This would be more than enough for this project.

The advantage of using a USB-C connector would be that a power adapter with USB-C could be used.  These will probably be quite standard in the near future.  At the time of writing (2018) these are still expensive.

There are more drawbacks: to get the 20V/5A, the device delivering the power and the device sinking the power must communicate with each other using BMC-coding.  This is implemented in the Richtek RT1715 and the TI TUSB32x family.  These devices are still rather expensive.  The SMD packages are small and hard to solder by hand.

Using this connector would be a typical case of over engineering.  There's no real advantage is using USB-C only for powering a device.  The exception could be for powering an electric razor.  You could use your phone charger to power it.  It saves you one power adapter in your luggage.

DC jack

Cheap, readily available, reliable...  The drawback is that there's no guarantee about the voltage level and polarity.  The user can connect whatever (s)he likes.  It's up to the powered device to cope with this.