Choosing the right Capacitor for powering Esp 12-E using AMS117 3.3V

After reading the data sheets that suggest no particular output caps and reading a lot of other things I decided upon asking it here
What is a good combination for capacitors both input and output of AMS 1117 3.3V?

Considerations:

  1. Powered by a 7V/800mA SMPS supply.
  2. The current requirements of ESP is no more than 300mA

Some Schematics Online:

Will be adding a decoupling 100nF cap between the output to the above schematic. But the real question is that is it a good option to use a big cap like 1000uF? I found this on a page using this circuit for powering the esp. Link to the page.

Another Schematic which i found is:

Is the latter one a better choice? More importantly why would it be? And can I use Aluminium Electrolytic Capacitor instead of tantalum?

There is an EEVblog video about decoubling capacitors. I recommend it.

That said, I recently powered an ESP + DHT22 wit a HT7333 with, due to a lack of anything else, 10uF+100nF MLCC in 0603 packages. LDO under the Wemos D1 Mini, DHT22 directly next to it. Especially reading the sensor totally failed. Every few days, also the ESP crashed. This problem is completely gone since I added another 100nF MLCC + 22uF tantalum at the DHT22 (but also within a cm to the LDO).

The datasheet of the AMS1117 suggests 22uF tantalum. 100nF are always good. I would go for that.
I diagnosed a power problem since the system worked when the D1 was plugged into USB.

is it a good option to use a big cap like 1000uF?

No. Really big caps are for getting rid of low-frequency ripple, like you'd have after a transformer/rectifier in the AC side of a supply. Caps after a regulator are to meet the stability needs of the regulator and short-term current spikes in the load, and I'd normally expect them to be less than 100uF.

ElCaron:
There is an EEVblog video about decoubling capacitors. I recommend it.

That said, I recently powered an ESP + DHT22 wit a HT7333 with, due to a lack of anything else, 10uF+100nF MLCC in 0603 packages. LDO under the Wemos D1 Mini, DHT22 directly next to it. Especially reading the sensor totally failed. Every few days, also the ESP crashed. This problem is completely gone since I added another 100nF MLCC + 22uF tantalum at the DHT22 (but also within a cm to the LDO).

The datasheet of the AMS1117 suggests 22uF tantalum. 100nF are always good. I would go for that.
I diagnosed a power problem since the system worked when the D1 was plugged into USB.

Which EEVblog video do you mean? In Episode #859 the theretical concept of chaining capacitors will be explained, but not which values to put in.