The battery size will affect only its duration. If you get a 1Ah battery it will discharge in approximately one hour if you draw 1A, half an hour if you draw 2A and so on.
The second formula is good, keep in mind that cheaper UPS have a square wave output instead of a sine wave, some devices may be affected. The radio might keep some noise from the UPS and the fan might not work well since these electric motors usually expect a sine as input. You are safe to try them anyway, no risk of frying anything.
To calculate the battery duration you should proceed as follows:
$$I=\frac{P}{V}$$
where P is power, in W, and V is voltage rms, in V. This formula is valid only if the load is resistive, in the AC domain things can get a bit more complicated, your appliances should report maximum current consumption on a label somewhere, use that value. After that:
$$T = \frac{C}{I}$$
Where T is duration, in hours, C is battery capacity, in Ah or A times hours, and I is current, in A. The computed time is not the actual duration you would get but it's the upper theoretical limit.
If you live in europe and your radio is approximately a resistive load it would draw about 40mA, so a 1Ah battery would last no more than 23h15m.