#1 most important thing.....TIRES. #2, alignment. #3, shocks.
The Mazdaspeed lime green shocks are similar to the Tokico Illuminas. The MSP shocks are Tokico blues (non-adjustable) If you can't get the Mazdaspeeds (our will be for sale sometime in August if you can wait for them), go with the Illuminas. In fact, you reallly only need them in the rear, where the stiff setting acts like a rear sway bar. But you still can stay in H-Stock (rear sway bars aren't legal in Stock classes)
If you want to do well in autocross, you need to build the car for the class. My advice is always to start in the stock class and spend your time/money on driving schools and tires, tires, tires.
Removing the front sway bar is fine for daily driving. It will make the car lean more (not too bad though) and it will also understeer less (similar to if you were to add a rear sway bar).
The rear sway is the ultimate solution, but it moves the car into a $$$$ class where you won't be as competitive.
BTW, you don't need to actually REMOVE the front sway bar (alot of work!), you just remove one of the end links (your choice either the left side end link or the right side end link....it doesn't matter) That way the bar won't flop around and come into contact with stuff. Well.....every once in a while if you drive into a steep driveway or something, you might hear it go clunk, but it's very rare.
Good luck!
NOTE: I wouldn't recommend running the car on sticky racing tires (street tires are okay) with the front sway dissconnect and stock (worn out) shocks. The car will lean too much and there's a very slim possibility it could roll over. Good shocks will elliminate the problem by controlling the sway. People are always amazed with how much good shocks make a difference.