What will replacing my front stock anti sway bar do to my cars handling?

Adding a stiffer front bar and doing nothing with the rear suspension will most likely result in the car handling worse, not better, near its handling limits due to the increased understeer you'd induce with only a stiffer bar at the front.

In general, adding more stiffness to the front bar results in less front roll but also more prominent understeer when the car is pushed near its limits in a turn. Adding more stiffness to the rear bar will result in less rear roll but more tendency to oversteer when pushed to its limit in a turn.

So the reason you'd want to tweak/tune both the front and rear bars at the same time is to get the benefit of reduced roll at all 4 corners of the car while also basically canceling out the increased tendency to understeer at the now-stiffer front with greater tendency to oversteer in the now-stiffer rear. Good suspension tuning is all about balance between all 4 corners. Changing the roll rate of the front and doing nothing to the rear rate would create worse balance, not better balance... and a poorer handling car at/near the handling limits as a result.

Once you spend another 11k on upgrades, your old brick will shine like the sun. But you already maxed out your credit cards. So what can you do?

Time to have a garage sale?

Dude the vehicle is top heavy. It's not a sports car. That's the wrong vehicle to try and corner with.

Yeah, changing the anti sway bars is going to turn your box on wheels into a track monster. These parts and fitting them is probably going to cost as much as your car is worth.

Update: Of course, swapping these parts will all of a sudden allow you car to turn like a fly.