The choke resists a change in current in a passive manner; no electronics needed as in the modern DC welder which electronically attempts to maintain a set current by adjusting voltage. I have the choke in the ground lead right at the battery, but I will move it to the electrode lead for the final setup. Anywhere in the welding current path will work.
It helps stabilize the arc as follows: as the current of the arc is starting to be interrupted, the choke will increase the voltage and thus help keep the arc going. Likewise, voltage and current will be reduced by the choke in case of starting an arc.
The modern DC welder is capable of doing this electronically, using high frequency PWM from an excessively high voltage. This keeps things compact and lightweight, but generates massive high frequency EMI from the high current, high speed switching. Just like a typical switch mode power supply, but at 10-100x the current. Emission strength is related to current times frequency times current loop area. The welding cables radiate this EMI, and the welder is very close. Ignoring what this does to the welder, the electronic regulation of current is a technically marvelous; no massive, expensive 40 lb choke is needed.
If you have a voltage monitor on your DC welder, you will find that welding is taking place around 20 volts plus a bit at 100amps of current. Current will increase dramatically as voltage is raised. I think that solar panels have insufficient voltage regulation, so while a bunch of 24V panels in series might work with a choke, I think the voltage may be too wild; open circuit is 44V. If your peak welding current is 125 amps this would still require 3000 watts of PV or better in parallel. I don't have enough PV to try it.
Welding cable size is determined by your max welding current. Small units with 140A limit may use 4 awg., 250A typically use 2 awg., 300a use 1/0. The point is to limit voltage drop in the cable and cable heating. I've ordered some 2 AWG cable, and will have short, 12 foot cables since the batteries with choke are going to be wheeled and portable.
Here's a link to the article which encouraged me to try a choke on a 2 battery setup:
https://weldingweb.com/showthread.php?8996-Welding-With-Car-Batteries-%96-2-ARC-STABILIZERThe one thing he didn't get right was his choke core; ferrites are never used for high current chokes as they saturate easily so that testing by LCR meter (testing with tiny current) will read way higher than the actual loaded inductance. But since he related his methods and materials well, it was a most valuable and well presented piece of research. I have experience re-purposing toroidal transformer cores as DC chokes, since I used two in my inverter project (for keeping ripple off the 120VDC), and could compare them to a commercial E-I core choke made by Hammond. Gapped laminated toroid cores have the advantage of being the most compact and lowest loss for high current, relatively high inductance DC chokes. Still, not cheap or lightweight.
The choke, with 22 turns (16 feet) of 6 strands of 12awg is shown in the attached photo wit the 2 group 29 marine deep cycle batteries. It's a 1000 watt transformer core, with a gap cut via abrasive blade, epoxy filled. I think it would work as well with only 8 feet or 10 turns and would be less likely to saturate at higher currents. Battery jumper cables were used for initial testing and will be replaced with proper welding cables and connectors next week. I will be increasing all the battery connections to some old 1/0 wire I have, with lugs added. The welding cable with use the standard Dinse 10-25 connectors at the to be designed battery& choke rack/cart.