Any carb progress??? Are you familiar with true plug chops? Throw in a new set of plugs and ride around for about 20-25 minutes. Find a safe and proper location to do wide open throttle for 10 seconds preferably uphill on a straight and deserted road, hit kill switch, pull in clutch, and close throttle all simultaneously. pull plug(s), put in spare(s), ride home.
now at home, clamp the plug hex in a vice, and use a hacksaw,sawzall, or portaband saw to chop the threaded portion of the plug off down to the porcelain,cutting, rotating plug, cutting, rotating plug, then eventually you can slide the threaded portion with the ground strap and all off the end and expose the entire porcelain insulator. for Wide open throttle main jet sizing, you should see just a light tan ring at the bottom of the exposed portion of the insulator. If it's too lean, then the thing will be really light colored with very little coloration, and you may see little speckles of vaporized aluminum (from your pistons!) on the porcelain. This is dangerously lean. Best to start on the rich side to be safe. If way too rich, it will be black and sooty. A little too rich and you will have the bottom half of the insulator looking pretty dark, but more tan towards the tip and electrode.
Plug chop info here:
http://jetsrus.com/FAQs/FAQ_spark_plugs.htm
http://www.xs11.com/xs11-info/tech-tips/maintenance/carburators/68-tuning-carbs-by-reading-spark-plugsthrottle-chop.html
http://jetsrus.com/FAQs/FAQ_rejetting_101_how_to_rejet.htm
http://www.strappe.com/plugs.html
http://www.dragstuff.com/techarticles/reading-spark-plugs.html
You do have to have the bike in a remotely decent state of tune to start doing that. First things first, you need to make sure the valves are adjusted and that you have even compression across all the cylinders. you'll need a compression gauge, feeler gauges, and probably a very handy Motion Pro valve shim changing tool. On Suzuki;s, they come in .05mm increments, and I think .03-.08mm is the cold tolerance. Has to be done when the engine has sat for at least 6 hours not running. The valve to cam clearance will get too tight over time with wear, and the valves will not seal tightly against the seat, or sometimes the seats get worn or burnt and then the valves get too loose where you have a big gap under the cam lobe. You are rotating the engine until the lobe of the cam is pointing up at the sky, and then check the clearance under the cam to the shim.
Then you need to get the idle set up right and the carbs at least bench synched, if not vacuum synched with a differential manometer setup. ride around at only 1/8 throttle or less for 20 minutes, and then pull all the plugs and note the color. No need to "chop" them for low speed throttle, you look at the top of the plug for low speed. mid range, you are looking at the middle portion that is under the threads, which can sort of be seen without cutting them. Full throttle is where you need to read the very bottom of the insulator that is exposed to the combustion. Play with the idle screw (it's an idle air screw on these carbs I think? Some are idle fuel, some carbs have both).
Here's a rebuild manual for this style of GSXR carbs
http://www.gixxer.com/forums/showthread.php?p=2374074
The main jet sizing does somewhat affect the needle height, so don't spend too much time with the needle adjustments after getting it to idle, just get it to run decent at 1/4 to half throttle playing with the needle height. Then go to the mains, get the WOT jet size dialed in the ballpark first just by riding it and getting a feel for what makes power and what bogs down. Start big & go smaller, too rich is safe, just dirties the plugs. Too lean melts pistons and burns valves! I think people are saying that 120-130 (Mikuni sizing) is in the ballpark. Was it 122.5-125? JetsRus.com sells affordable "OEM Equivalent" jets that are Mikuni copies at half the cost, so you can play around with the sizing without dropping a ton of cash. Start big.
After you get it feeling in the ballpark where it is making power at wide open throttle at higher rpm's, and once you are feeling comfortable riding the bike at potentially very high speeds, then you can do some true WOT plug chops on a safe deserted environment... With an out of true back wheel, it may not be so safe to do yet. Keep dripping penetrating oil on the threads of the spoke nipples for a while and then after a few weeks, deflate the tire to almost nothing and get a spoke wrench and start trueing. If the wheel veers out of true to the right, tighten spokes in that area that come off the left side of the hub, maybe 1/4 turn at a time. Also note where the dull sounding spokes (tap on them with the spoke wrench of something metal) are in relation to the bend. Unless the rim is physically bent, spokes loosen up and will let the rim go out of true to the opposite direction since the spokes on the other side of the hub are still pulling tight.
Be careful trying to do WOT plug chops, especially on an uncertain bike that you are just learning how to ride. Not trying to diss you, this is your first bike, right? In time it will all come together, mechanics and riding...
I'm really curious as to what jets you end up with to make it run good, as I have some 88-90 GSX600F BST31's and some 91-97 GSF600F BST33 Slingshot carbs for a 673cc GS550 project, and an 844cc GS750 project (track bike? building it from all my spare parts), and mainly because my buddy is looking for a set of BST33's or 34's for his 82 CB750 with the p.o.s. stock 3 jet aluminum slide piston carbs. He is constantly fiddling with the stockers and wants me to bring my BST33's over to try to get his bike to run right. I think he's ready to swap the GSXR carbs on...
Best of luck.