I personally always start off with the character's function in the story. I always try to fit them into their major position, their main function if you will. This doesn't really determine any looks or character traits at first, it's basically just "I know where I want to display the canvas once I'm done with painting" and it actually helps to keep the character smaller at first, because at first they're just a mere tool.
Then, I'll try to go from what I already know, you can always spot links to other characters, kinda like "that acquaintance of a friend of a friend" - you know superficial data of them without ever meeting them, you maybe know how X feels about them and that Y got his job from them because they are related. So while you don't know what they look like, you somehow still can deduct the following questions (at least in some way)
- are they a child/somehow related to someone already existing?
- who are their social groups? friends? enemies?
- any specific ethnic background(s) and culture that adds to it?
If you already have related, especially closely related, characters, it's easier to derivate their looks from them just by playing random genetics. Ethnic backgrounds can help as well, however, it's not as set as having parents or siblings already. Apart from genetics, though, culture can go a long way in how we for example dress and behave. Or why we reject certain things from our culture can tell more about our personality and character.
The thing is, if I know at least a tad of their genetic pool, I'm usually just going wild with it, kind of like the randomize button on dress-up dolls. Because that's usually how people just come to be: a wild genetics cocktail. This is why I rarely change designs of their faces from their first draft, unless their ethnical/familiar background changed as well. The rest can be adjustable through different things like clothes, mannerism, and lifestyle. This doesn't necessarily work with every art style, like very stylised cartoons probably won't work that way and go more by shapes, but I think this approach works perfectly fine with semi-realism.
The thing were aesthetics come into play is more or less the last stage where I get to know the character better and develop a feeling for them. Discovering more of their personality and thus also how they most likely would dress can take a bit longer or is immediately there - it really depends. I find it important to stress that it is an aesthetic your character likes and agrees with, or came to wear by one or another reason that makes sense for that specific character.
For the loving your own characters ... for me, it always happens when I make them out less than they end up to be. You need to discover their potetial.
One of my favourite characters in my story is Mae, who innicially should just have an appearance of three panels and just return a lost item to MC. The three panels just didn't feel really organic, so I ended up with 8 pages of her being a grumpy morning person, discovering the lost item, and not even returning it yet. Through the dynamic with her room-mates and the fact that she knew MC enough to know how important that item was, made me spun stories around her. She turned out to be one of the 4 MCs from the main series and I'm currently working on a spin-off completely dedicated to her silly teenage romance because I couldn't fit it into the main series as much as I tried.
I think as soon as you realise what person they are, what storylines could still be waiting for them, what else you still could explore with just this character, the more invested you might actually get. At least that's what is always happening to me..