Here's what I did in case someone finds it useful (I used a lot of things according to the rest of the answers in this thread):
First I adjusted the layout settings as needed. This changes the window size immediately so it was easier to set the exact size that I wanted. By the way I didn't know that I can also have visible width smaller than width buffer. This was nice since I usually hate a long line to be wrapped.

Then after clicking ok, I opened regedit.exe and went to "HKEY_CURRENT_USER\Console". There is a new child entry there "%SystemRoot%_system32_cmd.exe". I right clicked on that and selected Export:

I saved this as "cmd_settings.reg". Then I created a batch script that imports those settings, invokes my original batch script (name batch_script.bat) and then deletes what I imported in order for the command line window to return to default settings:
regedit /s cmd_settings.reg
start /wait batch_script.bat
reg delete "HKEY_CURRENT_USER\Console\%%SystemRoot%%_system32_cmd.exe" /f
This is a sample batch that could be invoked ("batch_script.bat"):
@echo off
echo test!
pause
exit
Don't forget the exit command at the end of your script if you want the reg delete line to run after the script execution.