Yes, 125Ah means something

Far more than "tiny diode", "skinny wire" etc

Assuming you want to prevent damage to your batteries, you should limit their draw-down to < 50% of their rating. Connected in parallel your maximum storage is 250Ah, and your nominal usable storage is .5 * 250 = 125Ah. @ 12V a 125Ah = a nominal 1.5kWh output. Suggesting that you could draw 75W for up to 20 hours. If you are running an inverter from your batteries and a device rated @ 75W from the inverter you could get from 40% to 75% of that run time, or 8 to 15 hours. (Assuming the batteries were at full capacity when you began.) In comparison, 1.5kWh from the grid should cost you between $0.10 and $0.30 depending on your local rates.
Power generation is an economy of scale phenomena. The larger the scale, the more economical. IMHO a sub 25kW wind turbine located in an area that has less than 8m/s sustained winds is a hobby oriented pursuit. As such it is not likely to ever recoup the money spent on it. I know there are tons of people who would argue with that statement, but it is based purely on the numbers. Even large-scale commercial wind turbines require careful consideration of location and government subsidies to make them economically viable. Having said that, I think wind turbines offer the most promise for viable RE. I also think small-scale wind mills (<25kW) help people realize exactly how much power they waste, and creative ways to reduce their consumption. Small-scale wind turbines also offer a viable power source for remote locations where the grid is not available.
It is very difficult to determine your charging rate from the figures you have given. What we would really need is the Volts and the Amps. Your Batteries are "clamping" the voltage, so you could be inputting as little as a few milliamps, or you could be inputting 20A, though I suspect the former is more likely. The power stored in your batteries is measured in Amp-Hours, there is a semi-linear relationship between the stored power and the number of amps in and out. The charging/discharging processes incur losses which means that 10A in does not give you 10A out; and in the real world the batteries charge best at some input curve that has nothing to do with available wind
Using your "skinny wire" as mentioned above severely restricts your Amps to the charging system. Power Lost = Amps ^2 * Resistance. The thinner the wire the higher the resistance, hence if your "skinny wire" has a resistance of 1 ohm (.00473 * 100 * 2 = 0.946ohms) you are loosing power as per the following table:
- Code:
Wire Loss
Power to to Used Wire Loss
Resistance Current Wire Loss Batteries Power System
Ohms Amps Voltage Watts Watts Ratio Percentage
1 1 12.5 1 12.5 8.00% 7.41%
1 2 12.5 4 25 16.00% 13.79%
1 4 12.5 16 50 32.00% 24.24%
1 8 12.5 64 100 64.00% 39.02%
1 16 12.5 256 200 128.00% 56.14%
1 32 12.5 1024 400 256.00% 71.91%
Where:
Wire Loss Power Ratio = Wire Loss/Power To Battery
Wire System Percentage = (Wire Loss) / ((Wire Loss + Power To Battery)
Of course, if your diode is only rated @ 1A or less (as it likely is) then increasing your wire size may well destroy your diode
Anyway, it sounds like you are having fun and learning. Those are the important things; you aren't likely to impact your power bill much with your hobby regardless of how efficient your system becomes

So enjoy it and learn!
Fish