bassmansrc

Adding to the other comments...

On camera flash, with an underexposed background (especially in the second two photos).

• Put your camera on manual.
• Set ISO closest to base ISO for your camera (ISO 100 for Sony for example), though if you are finding that you can't get the exposure you want at the base ISO(after adjusting the other settings mentioned below)...like maybe if your flash is underpowered...then feel free to start raising this ISO until you get what you are looking for.
• Set your aperture to the level of Depth of Field you would like (how much do you want in focus). Looking at these pics, I'd say something reasonably higher like f11, maayyybeee f8
• Set your Shutter Speed to a point where it blocks out most of the ambient light. This will totally depend on the environment and level of ambient light that exists for your scene. But start with the max sync speed for your camera with a flash (for Sony that is 1/250). If that cuts out too much ambient light, just decrease the shutter speed until you get the background exposure you are looking for.
• Finally, set your flash to the exposure you want. These look like they might be a stop or so overexposed so I would set it to the highest power and then move down until you hit the mark you are looking for.

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