You may want to consider a AC-DC converter off-the-shelf. The reason why is that 220 VAC converted to DC is 311 VDC, quite a shock hazard. Switching power supplies need expert design engineering. We have helped many with LED supplies, but not at such a high voltage (180 VDC). Most DIY stuff for LED's is limited to 100 volts.
Yes, that first link (MP4001) would be a good choice. The limit would be the voltage and max current of the MOSFET that drives the LED's, which can be any color by the way. Just remember that this is NOT isolated from the main AC supply so even touching an LED could be a shock hazard.
The second link (AL9910_A) seems like a mirror image of the first, but it has a much more complete datasheet with warnings for this-and-that. Buy a 500 volt MOSFET rated no more than 5 amps. The reason is that 'beefy' MOSFET's tend to need a lot of drive current, which these tiny IC's cannot do.