Welcome to flash photography! My photography took a ginormous leap forward when I truly learned how to use and control off camera flash.

If this is your very first flash, then my suggestion is to not worry at all about round vs. rectangle. Not important.

What is important is to really learn how to work with flash…how it impacts your setting choices, how to balance it with ambient light, how to use it to control the scene, create the shadows you want, highlight the subject in the way you want, etc.

My suggestion:

• get the cheapest flash that works with your camera. Look at Godox offerings for example.
• ignore TTL modes…instead keep the flash in manual and spend a good amount of time really truly learning how to balance the flash settings with the camera settings (endless YT tutorials available for free). Nothing wrong with TTL modes per se, just like there is nothing wrong with auto modes on the camera. But, when you really understand how to fully control the manual settings on both the camera and flash in order to get the photo you want by having this new found control over the light, you will find yourself with this confidence in shooting that can’t be bought.
• The reason I say go with the cheapest one to learn on is because if you really do learn off camera flash, you WILL end up wanting to upgrade and expand. At that point is the point to start investigating the minutia of difference between flash features (such as round head vs rectangle). Also, at that point is when you say RIP Bank Account. lol