If you are interested in carbon, I would highly recommend the Misono Swedish Steel. I have had the 240mm (about $170) over a year and a half (used professionally) and am very happy with it. I let it develop a natural patina, which happens very quick for me. I'll use a rust eraser every so often, usually every couple months when I thin it and take off half the patina anyway. I'll use it for everything now, mostly veg tho (entremetier haha). I use it on acidic fruits and onions all the time and don't have a problem. I also have a habit of constantly rinsing and wiping my knife, even before using carbon. It's just more sanitary. There was only one time I had it rust. I left it on a back prep table during service and when I was looking for it at the end of the night I had found someone first moved it then someone put a water bath on top of it. It had spots of rust and pitting, but it still works just fine. It holds a good edge, too. A few months ago I lowered the angles on it and got it super sharp and still held its edge about as long. I try to sharpen once a week up to 8k and use a polished steel the first couple days then switch to a messermeister ceramic. The ceramic can keep it going up to two weeks when I get lazy haha, although I try not to do that. It comes nicely sharpened ootb, but can be made sharper of course. At least in my experience it is one of the lightest and thinest western handled 240mm gyutos I've held. It also has a very nice flat profile.
The Masamoto HC is also very good, and supposed to be a little better providing you can sharpen it well enough. It may be a bit thiner than the Misono, but about the same weight. Really hard to notice a difference.
The Gesshins are all very nice, and may actually be my next knife haha.
Don't have many recommendations on stainless knives. I have a 440 Misono petty and like it, but I think most of the stainless Misonos are overpriced for most knives. The moly line petty may be worth a look tho.
I don't like Shun. They are fine knives, but very expensive for what they are. You can get equal or better for less. Also, they have a much more rounded profile, which some like, but I don't.
For pairing knives and bread knives, cheaper is probably better. I use forschner for both and they work just fine. At least for a pro, pairing knives tend to go missing rather quickly so it's not worth spending much on them.
Whatever knives you choose leave room in the budget for stones. Not much of an expert on types/brands here, but I'm sure someone else knows. You can get a 1000/6000 stone for well under $100 and would be more than adequate. A stone flattener is probably like $15-20. A good steel is also important. Anything grooved or diamond is bad and just files away the edge and making lots of coarse "teeth" and chips. The best are either smooth/polished steels or ceramic and used properly, of course.
Good luck with your search, and once you get proficient at sharpening, any knife will work great.