Go get some popcorn and sit back for a read. This is going to be long.
So, bang for the buck updates...here are my thoughts. I'd proceed down this path using Firm Feel or Hotchkis parts as they can be bought one at a time to facilitate the evolving you car will go through. All of this is also predicated by having a solid, functional system that doesn't need simple repairs like ball joints or bushings. If any of these are suspect, the very first thing to do is rebuild the suspension. $300-1000 depending on if you do it yourself of have a shop do it. If you have to do this step first, then opt for the Moog offset upper control arm bushings. Install these opposite the instructions to obtain more caster instead of more camber.
First is to create a solid foundation for all the improvements to work off of. You need to shore up the flex in the car to allow the suspension to do its job. As such, the minimal starting point for this would be subframe connectors or a set of torque boxes. You can get as fancy with this as you want from basic 1x3 tubing to contoured connectors. If you want it to all look stock, the torque boxes can impart a stock look that helps firm things up over nothing at all. I'd say these are minimum to start with body bracing. You obviously can add even more pieces in more areas to really step up creating a solid car, but you need at least this first step. Firming up the body also has the side benefit of reducing squeaks and rattles, allow panel gaps to remain constant, improving window seal and reducing wind whistle. Costs for this can be as low as $20 if you cut and fab and weld your own to a few hundred for custom fit contoured units that someone else installs.
Wheels and tires are obviously the biggest improvement you can do. They also are the most expensive single purchase of the entire process and will consume half your entire budget. So this would either be the very first thing or the very last thing I'd do. Typically I do them last. If you do them first, it will help some with grip, but it is still dressing up a turd as the systems underneath it all can make the 14" tire set up feel significantly better while 17" tires on a tired suspension will still feel floaty, wander, and bottom out. Probably will be even worse as most guys step up width in addition to diameter, so you get the double whammy of bad suspension combined with wide tires that will make the wander even worse. So $2000 or 50% of the total budget for this update and it can be thrown in at any time during the process.
Along the same lines as tires are steering boxes. Again, first or last, but I'd do it last. Steering boxes don't do anything for actual performance increases, but they do make a world of difference in road feel. They also are expensive as a Firm Feel units will run around $500 exchange or the ultimate box approach may be a Borgeson box and related hardware. This is a late model style box that will really change the feel but will also set you back $1000. That's 25% of your budget. IMO, I'd try the shim trick posted earlier and swap out the box much later down the line.
If you go with the first two mods above as your first choices, then you potentially only have $500 to play with for the rest of the upgrades. This is why I would tend to put them further down the list.
Aside from that, the very first thing I'd do is get a radial friendly alignment. While this may need to be done again after some other changes, sometimes simply doing this entirely changes the personality of the car. If you have a good shop, they may have already done this, but odds are, they probably didn't. Ask for 2000 Mustang specs to simplify the process. These keep your shop tech from being confused about the uniqueness of the mopar set up and putting the OEM specs under, especially if they don't do custom work. OEM alignments are for skinny bias ply tires. Unless you are using Firestone Wide Oval repops, avoid factory specs. If your shop does do custom work, you want 5* positive caster, -.5-0* camber, 1/16" toe in, or maybe .08* toe in. The reason for this is positive caster increases stability, creates more dynamic tire orientation during suspension cycling, and helps increases road feel. The negative camber also increases the tire's ability to stay in touch with the road surface, especially with softer torsion bars. The toe minimizes wear while keeping the tires as straight forward facing as possibly with all the joints in the steering system. $40-100 depending on your local shop rates.
After that, better shocks. Since you want a good handling street car and don't plan on racing, there is no need to get crazy with adjustable units. The RCD Bilsteins would be great for this. $400 for this update. If you are really in a pinch, Monroe Gas Magnums can make do and can support increased torsion bar rates under 1" if you go there later. These are only $100, but the Bilsteins are a huge improvement so I'd encourage you to use them instead.
Next, a stepped up front sway bar. The tubular units are a nice step up in performance. $300 here. You can add a control arm strap or plate to help apply some of that force as well as the bigger bar imparts a big increase in force on the lower arm. Compared to the stock .875" bar, a 1.125" solid or 1.25" tubular bar is going to do a lot of controlling body roll in corners and imparting a more confident feel.
Since you already have a rear sway bar, you can skip this step as normally I'd suggest adding one here. New Hellwig and Hotchkis models can be adjusted to further dial in feel, so that is a nice position to be in, but is not a requirement. This saves you a couple hundred bucks.
After sway bars, if you still want to add improvements, then this is where some stepped up torsion bars and leaf springs come into play. Moving up to 1" diameter t-bars will match nicely with the previously selected shocks and provide a big step up in wheel rates that are much more late model in feel. Hotchkis does suggest 1.12 for their components and it certainly can be felt. Torsion bars may be found as cheap as $200 but will most likely be $350+
Stepping up the front without a comparable step up in the rear will typically produce an unbalanced car that understeers worse than stock. I'd suggest changing leaf springs to match the torsion bars are the same time or at least in stepped replacement with each other. This is where the matched sets provided by Firm Feel or Hotchkis are help full. There are several sources for these. Expect to spend around $400-500 depending on how customized you want these to be.
So there is the basic formula for a solid cruiser:
suspension rebuild $400
sub frames $150
alignment $100
Shocks $400
front s-bar $300
rear s-bar $200
t-bars $350
leafs $400
Wheels & tires $2000
total $4300
Obviously you will have savings if you don't need a rebuild from start, have the rear bar, or pick up any deals along the way and this goes up if you decide to pull in steering box swap or substitute tubular control arms for items you don't need as part of the package.
Out beyond that are incremental improvements that are going to produce that Nth degree of feel that most drivers can't differentiate and certainly aren't pre-requisites for the biggest step up in improvements, but can certainly help improve things further. Among these would be tubular control arms - biggest gain, extra caster, $400+. Some would argue that these should be part of the list above. I might conceed that if your alignment specs are really crappy right out of the gate. One of mopars achilles heels is the lack of our ability to get decent caster numbers. Tubular upper control arms are built with extra caster in them and combined with different adjustment features and the stock eccentrics, can easily achieve 5-10* of caster . This is one part I'm kind of torn on not recommending right out of the gate but it is really a variable form car to car.
Solid tie rod sleeves or stepping up to 11/16 tie rods- $200 for reduced deflection under heavy corner loads.
Welded K frames -$ is variable if you can do it yourself or have to pay. This falls under flex reduction which is always a good thing, but unless you're tearing your car apart, this is a tough one to accomplish without putting your car out of commission for several weeks.
Pitman arm bearing/brace - $135, again, flex reduction and more pointed steering response. IMO, thi s is a decent upgrade if you never plan on welding up your K frame. This bolt in very easily on completed cars.
Ider arm bearings - $125, part of a smooth steering package.
Fast ratio arms - $300 this does speed up steering response. Great for low speed parking lot racing or tight confine parking, but not a prerequisite.
Adjustable strut rods or fixed pivot strut rods - $200. These can help fine tune caster and do help reduce toe changes under heavy breaking. Not bad things to have and certainly necessary if you ever push the car through cone racing but not required for a cruiser.
Other changes like offset springs, drop spindles, special brake compounds, so on and so forth get into the how far and how hard do you want to push improvements or any individual quirks we have about having something we fancy.
So, my opinion on spending your money. I'm sure others may agree or disagree. Your mileage may vary as well.