Beket, just so you know, pretty much anything you do will void a warranty here or there. Especially messing with the ECU. Depending on how cool your dealership is (like maybe they sponsor rally/auto cross cars or something and know it's all good) will you get away with it. I have the AP and love it. You can just start with the stage 1 OTS (off the shelf) tune and feel some power increase while running totally safe. Stage 2 is where you might run into more scrutiny from dealerships should anything happen, but if you're like me and install it yourself, then you can simply uninstall it prior to the trip to the dealership =D I'm very happy at stage 2 right now and haven't have any issue taking the car in for anything, but my service manager and mechanics are pretty cool.
As for the understeer, yeah, that was a big issue I addressed immediately starting with a rear sway and end links. Typical healthy set up is going to be 24mm bar up front and a 22mm bar in the rear. I like a little off road so I went 22mm up front and 20mm adjustable (gets stiffer if I want and have it on the middle setting right now so it's pretty balanced). Honestly I could go back to stock because the more play the better when you're taking bumpy sections, but I just like dirt and mud, not serious off road, hahaha. Sways and end links decreased the body roll considerably and also balance out the handling (like you mentioned starting with understeer, but if you get too rear bar happy you will end up with over steer instead so study up on it before you pull the trigger on your set up!).
The short throw shifters will make your stick move less distance to engage the next gear, making faster shifts possible. It also adds a degree more effort to shift, but feels more purposeful in my humble opinion so I really love the feeling. Unfortunately I like the stock height of the shifter so there are adjustable shifters that cost more if you're like me. Otherwise they are straight replacements for the stock one that sit closer to the tranny and have a different position for the bushings and attachment to the throw arm that makes the shift happen. A very nice mod indeed I'd say. I used the Perrin attachment STS adapter deal and it is nice to get a feel of shorter throw with the same shifter and stock height, but not quite the real deal if you follow. It's a nice start though for sure and cheap, lol.
There are a bunch of good builds with excellent write-ups on how they went about choosing their parts so you should study up on them (uhem, boost addict) to find out some more. Here's a link to a very thorough guide, but keep in mind it includes all makes and models so don't swear by it that what worked awesome for a 2004 sti will be good on yours = Unabomber's Manifesto - NASIOC
Finally, Welcome to the club!!! Hope you have fun with it and don't get bit too hard by the mod bug or you'll have 350 WHP before you know it and an angry wife, rofl!