Can I create a private model just for my personal use?

I am very new and just dabbling at the moment. I would like to try my hand at all this and create a model or two to start out, but I don't want them to out there in the world just yet. Can I create a private model? I feel like I should, but I haven't noticed that option yet.

If you mean creating a model with the onsite LoRA Trainer, then yes. You will have an option to publish the finished model, but it is not mandatory. You can simply download it and use it yourself. It won't be 100% private though, as the staff also has access to it so make sure your training images and the content of the model are not breaking the ToS.

Since you didn't specify the type of model, in addition to LoRas, you can train or merge full models yourself. Actually training a full model can take a lot of power so if you don't have an uber powerful computer you likely would have to rent online GPUs. Merging on the other hand can be done yourself on your own computer. You can simply download various models that you like and then use Automatic1111 to test merging them in different ratios to make a model that has different outputs. At this moment I don't recall if the merge tab is a default tab or is you have to install an extension, but it is quite easy. It can be quite fun to see what you can make.