Battery Powered WISMO228

What Li-Ion 3.7V capacity is suitable to power the WISMO228 directly?

That depends how long you want it to last. The average GSM idle current is stated as 1.3mA. You can calculate your rough expected lifespan by using:

time (hours) = capacity (mAH) / average current (mA).

As long as your battery can supply the peak GSM current of about 350mA (most Li-ion can), you should be fine.

If you are powering directly from a battery, make sure you don’t exceed the recommended maximum voltage of 4.2V when charging, as this could damage the modem.