Say you have a lamp with 48 bright white led's. 16 strings, 3 led's per string at 20 mA.
At 12 V it will use .33 A continuous, or 4 W.
You need to power it at night for, say, 16 hours maximum. The batteries must store 64 W-hrs. At 12V this makes 5.3 A-hrs. A string of 6 'C' cells would be sufficient.
A charge session might be 8 hours. The PV panel must generate 64 W-hrs in that time. Hence a 12V panel must put out .7 A or more continually.
The least expensive part will be the control circuitry and light detector.