Shun aren't particularly good values. The chef's knives are designed with "German" profiles and unless that's something you particularly want it's a big negative. Talking about why is a good intro into the subject of how knives relate to knife skills.
I'm trying to figure out if I should steer you towards big name western handled, knives like Kikuichi TKC, MAC Pro and Masamoto VG; something wa and fairly mainstream; or wa and a little more esoteric, high performance but mid level cosmetics -- like a Richmond Addict2 in CPM 154 or even a Richmond AEB-L Laser.
Then we have to look at the issue of weight. Middle weight? Light-middle? Or, ultra light weight?
I used to reflexively steer people towards MAC Pro for their first, good, mass-produced, western-handled knives. It's still a great line, a big step up in performance from Wusthof, Henckles, etc., but not a wrenching difference in F&F, or knife ergonomics. But there are a lot more possibilities nowadays -- or maybe it's just that my own horizons have broadened.
A set with a MAC Pro gyuto, slicer, petty, and parer as well as a MAC Superior Bread knife; a (Forschner by) Victorinox 10" butcher knife, and 7" wide fillet or 7" curved breaker; and for sharpening an Edge Pro Apex Essential Kit, and Idahone "fine" ceramic rod -- is almost certainly along the lines of what you were thinking before we started talking. It would be a great choice... But maybe your horizons are starting to broaden as well.
My working knives are mostly wa, and of those about half are ultra-thin, ultra light "lasers." But I also use some yo meat knives. However, that's an example not a recommendation. Different people like different things.
By way of another example, I'm currently using two different "go to" gyuto. I usually choose on the basis of what I'm going to cook. One is the "laser," but the other is robust enough to border on what's called a "mighty gyuto." Each suits me, both suit me better. And where in the heck on the spectrum do we put you?
In any case I think you (and most people) should spend the most money on a gyuto; and possibly as much or almost as much suji. You won't use your suji as much as your gyuto but quality makes a big difference; so there's some prioritizing to be done there -- or maybe not because your budget is so friendly.
The cost of a really good bread knife isn't going to be much.
It's nice to have a good petty (6" paring knife), but because they take so much abuse and get sharpened so often it's not worthwhile to spend a lot on a petty -- unless you have other knives for the rough stuff. I don't use either of my good petty knives for packages or string. But both are tough enough to use for boning -- so...
Unless you do a lot of fancy tourne and other garde manger crap (and even then) spending more than a few bucks on a small paring knife is just throwing money away.
The two most important takeaways at this stage of the game are the importance of knife and sharpening skills. You seem to be sold on sharpening. More than convincing you to buy any particular knife, I'd like to get you using a proper pinch grip.