Voltage regulator circuit
I think you're overthinking this too much.


  My load will be an MCU drawing roughly 10 mA and RF module drawing 50 mA during transmits.


MCUs genereally don't care much about (ripply and noise) on their supply lines. Heck, these digital circuits are generally the ones that pollute the supply lines!

No, you do not need ferrite beads and/or inductors in your supply lines. That only applies for sensitive circuits when also RF (high frequencies) is involved.

Just follow the general rules:


add a supply decoupling capacitor (100 nF) between the supply pin of each chip and ground.
if possible use a large ground plane
add input and output capacitors as the manufacturer on an LDO suggests. The manufacturer of the AP2204 suggets 1uF and 2.2 uF so that's what you will use.
use ceramic capacitors unless these are too large and/or too expensive. 2.2 uF is fine for a ceramic cap.
If you need to use a non-ceramic capacitor for decoupling, add a 100 nF ceramic cap in parallel with it to improve high frequency behavior.


X5R ceramic capacitors are "good enough" if you use them for hobby projects. For professional use you might need X7R which are "better" but more expensive.

In general: if you're just playing with a micro controller for hobby purposes and nothing high frequency is involved then almost any capacitor will do the job. There is also no need to use inductors and ferrite beads.

Also: see what others do and do the same, there are plenty of microcontroller based designs / projects to be found. For example the many Arduino based projects, just copy what they do and notice how they generally don't use any inductors nor worry about the capacitors.