Solar Panel and Battery Management - 3.3V output
First off, the power you will get from the solar panel will depend greatly on where you mount it and which way it faces. You should assume that 0.5W is the max power you will get out of that panel on a bright sunny day (somewhere near the equator) with the panel facing the sun. So, derate the panel power accordingly. Assuming you're good on that count, you'll need to account for the inefficiencies of the battery charger, the battery itself (internal resistance, coulombic efficiency, self discharge).

Now for the BQ2512X:
The datasheet (slusbz9b/slusbz9b.pdf on the TI website) very clearly provides a reference schematic along with the layout guidelines as well. However, this chip is designed for a fixed input voltage system (consumer electronics), so the input voltage must be >3V. The system must choose the battery charge current using the  such that the panel terminal voltage stays above 3V. This means you will need a dedicated MCU talking to the BQ over I2C.
Also, I assume you know the BQ is only available in a BGA package, which may eliminate the possibility of hand-soldering a prototype.

To summarise, the BQ is probably not the best chip for this job. You might also want to consider getting a panel with a higher terminal voltage, but similar power.