Another consideration can be tank weight. I can't move around the 300s anymore. I have a 125 and it weighs about 60-70 pounds. The 300s were twice that. Also don't buy a tank that you intend to keep and refill. An exchange program with a local welding supply where you simply exchange your empty tank for a different but same-size filled one is a much better way to go. You will never have to recertify tanks that way.
How big? I have no idea how much you intend to weld. Having said that I think I still recommend a 125 and if you need more gas on hand then just get a second tank. I believe you can return the second tank at the end of a big project to the welding supply store, Ask them. This will keep the weight per tank low and still keep enough gas on hand,
For example, I tig-welded a complete set of headers for my SLC with a full 125. I also welded all my water pipes together for the SLC and back-gassed them (stainless requires back-gassing and more gas) with a full 125. My most recent project was a new set of steel engine mounts for my SLC. I started that project with only 500 lb/inch in the tank, and it was fine. They hold more than you think.
So my vote is a 125 unless you have a commercial requirement. Find a welding supply store and go in and ask about exchange tanks and available sizes. Where I live the 125s and 300s are the common sizes. You want to be able to take your empty back and exchange it the same day when it runs out.