j-v, thanks for the reply. I am not certain what size the iPhone videos are, as I just use the phone's camera in whatever the default setting is, but it is an iPhone 14 if that helps? I render output in 4:3 and everything renders fine with the converted video format included with some camcorder video and still pictures all as part of a project. Just hoping for a little clearer video image on the finished product.

j-v, thanks for the reply. I am not certain what size the iPhone videos are, as I just use the phone's camera in whatever the default setting is,

To show us what type of files you make you have to use MediaInfo and show us, following this tutorial:
https://www.vegascreativesoftware.info/us/forum/faq-how-to-post-mediainfo-and-vegas-pro-file-properties--104561/

I render output in 4:3 and everything renders fine with the converted video format included with some camcorder video and still pictures all as part of a project.

Format of the video you can choose in your program before rendering but where do you want to show or play that video in order to choose a rendertemplate and with that the needed codec for redering..

I am wondering if there is a more sophisticated way of converting iPhone videos to use on this older Sony product to get a little better iPhone video resolution quality, 

Probably not. Your video needs to be converted to constant frame rate, as well as converted to a codec that is agreeable with Vegas 12.

It won't cost you to download the Vegas Pro 20 trial and see if you like the results better. Be aware, though, that 20 won't convert your phone's DolbyVision, so just don't use it.

@monte1988 Which Handbrake "Default" are you using?

Good question. At the very least, @monte1988 should set the Frame Rate in Handbrake as "Constant / Same as Source" for use with Vegas 12.

I was also wondering about the Handbrake bitrate. But we need to have the source file's media info first.

I start with the Production Standard preset in Handbrake and tweak from there.

Okay when I look at one of my iphone video's properties on the phone it says the following:

1080p * 1080x1920 * 22.4 MB

I am guessing that this means it was shot in 1080:1920 pixels? I have yet to try the tutorial on what the output is, but I will when I can get on that PC. I turn the output into a DVD (old school, I know). For Handbrake the default is H.264 with constant bitrate. I can look further at those default settings when I get home. Hopefully some of this information helps? Thanks

I am guessing that this means it was shot in 1080:1920 pixels?

Yess and that we call "portret mode" .
Vegas 12 has not a build-in portret template to choose for a project.
That you must build by yourself unless the renderoutcome has to be something else, so it is also important to know what the goal is for your project outcome.