Setup for TPS78001 voltage regulator
I agree that the TPS78001 would be a good choice assuming you stick with using 3.7 V (one Li-Ion cell or more cells in parallel) as the battery.

Going for a switching regulator will not bring much as the voltage drop across the regulator is small. Also the quiescent current of a switched regulator is very likely going to be higher than the 500 nA of the  TPS78001.

To save power, I would design for the lowest regulated voltage both modules can accept so that would be 2.8 V. Then as long as Vbat = 2.8 V + 0.2 V = 3 V the regulator can regulate properly. But at 3 V the battery is too low anyway. Ideally you'd design the device to shut off if the battery goes below 3.4 V or so.

In the datasheet I only see 1 uF decoupling capacitors so that should be good enough, no need to add 100 nF. But (pro tip!) if you are designing a PCB for this then just add the footprints on the board but not place the component. Then if you do need them later, they're easy to add.

If you cannot calculate the resistors needed to set an output voltage then you're overthinking it. Look at table 2, note how R2 is always 1 M ohm.
Note how \$V_{FB}\$ = 1.216 V, it is a constant. If you want 3.3 V then \$V_{out}\$ = 3.3 V. Now use equation 2 to calculate R1.

You could also see it as: R1 and R2 are a voltage divider. The input voltage is 3.3 V and the output voltage must be the value of \$V_{FB}\$ so 1.216 V. That would give you a ratio R1/R2. Then you choose R1 (or R2, it does not matter) and calculate the other.