Trey, I am sort of a vegetarian myself and I had to deal with the same issue on eggs as well because they are a good source of protein that still fits well my ethical views (I don't like to kill stuff if I can avoid it).
So to answer your questions, what I recommend is:
On the issue of
quantity, a big problem is that eggs are good protein but it takes a lot of them to get enough proteins. A whole egg is ~6g (4 for the egg white alone), and if you are 175 and trying to build muscles you want ideally at least 175g of protein, which would be 29 large whole eggs. That's waaay too much for so many reasons, but most importantly because you will get sick of eggs after day 4 hehe.
What you should consider instead is varying your protein sources more and include some eggs as part of that. Proteins from dairy, especially as protein powders are much cheaper and concentrated, it's a lot easier to drink a glass of 50g protein drink than 8+ eggs.
On the issue of
preparation, again I recommend cooking egg whites (uncooked you throw away half of the protein essentially, see
link) and probably taking out yolks and just sticking with egg whites if you are going to eat a lot of eggs, because it's a lot easier to balance your total calories, essential fats and other nutrients using egg whites (basically pure proteins, while yolk has 5g of fat for every 2g of protein, not a good tradeoff).
Another note on what you call
'super-processed' foods like whey, they are perfectly fine especially if you know what you are doing and use them to supplement your diet. A multi-vitamin pill is super-processed too and is still a good thing to add to your diet, while there are plenty of unprocessed foods that are still generally bad for you or your goals.
Just look at what your diet is and how far you can get in terms of good food given your budget, taste and other practical considerations, then consider supplementing things that might be lacking, like fiber, vitamins, proteins, and even things like creatine. As a vegetarian, your levels of creatine are much lower than those of people who can get extra creatine just by eating meat, which naturally contains it. Also you might want to vary and alternate your protein sources based on how fast they are absorbed, whey protein more for workouts and slower absorption proteins like caseins overnight to give you a more steady and prolonged supply of aminoacids.
