<p>Looking to print a new part for a home appliance. There's going to need to be a new model created with the customizations made, but the model (after printing) will have to fit where the old part was. Is there any 3D modeling software that is better for this purpose? Will I just have to guess at proper proportions and hand-adjust the scaling of each dimension and angle through trial and error until a version fits?</p>

Thera are plenty of such guides. But from necessity they deal with specifics, there are too many things to cover otherwise.
Multiple types of printers, multiple brands, multiple slicers, multiple ways of modelling etc,. With more all the time. Reading up on something that tells me how to model and slice in Freecad & Creality, when I'm using Blender & Cura is a waste of time.
Generic instructions that apply to everything are so vague as to be essentially useless. (Plenty of those online though)