Every time my friend or I open overwatch nothing is loaded in. If you join a game within 5 minutes of opening it no characters will be loaded in. This only happens with overwatch so I know its not just my computer being bad, every other game is completely ready to go. I honestly think its really dumb that I have to start a random game to get everything to load in just to be able to see models and my own hero.
That is your PC not being quite enough to handle overwatch. I had the same issue until I upgraded.
That’s not something that has ever happened with my game. I’m not incredibly tech savvy but I do use a SSD which is maybe why I don’t?
Make sense to me in a way. It is likely loading stuff from disc to ram and will not load those things until needed.
It happens in my games too 
My “gaming computer” is actually just my homework laptop, so for the first few minutes, FPS is cut by like half. I usually just mill about in the practice range until I get a consistently high FPS, and only then do I load into actual games 
If you don’t have an SSD, I highly recommend buying one and putting your OS and OW on it, normally solves the load-in wait and helps with loading into a match for faster hero selection as well, plus 120-250GB drives are fairly cheap nowadays.