Trying to diagnose running problems on a bike with an unknown maintenance history can drive you crazy. Common maintenance items like clean carbs, properly adjusted valves, no air leaks in the intake system (airbox, carb boots), a clean gas tank (no rust), and a properly functioning petcock are 100% mandatory for the bike to run properly. It's best to perform all the bikes maintenance when you first get it, and then if problems show up, you will know what the problem is not.
A proper carb cleaning requires a full tear down, soaking the parts in carb dip (or ultrasonic, if you have a good one), and reassembly with fresh O-rings. Pilot jets, choke tubes, and pilot circuit passages, in particular, need a proper cleaning before the bike will run right. Even if the bike seems to run right, if the O-rings are original they are sure to be hard and brittle, thus problems could be right around the corner.
Whenever possible, buy OEM Kawasaki parts. They are sometimes expensive, so if that is a concern, get the PN from Partzilla, or similar, and then search eBay for a better price. Aftermarket brake system parts and gaskets are particularly risky (never buy green gaskets.)
The classic "hanging idle" (or idle speed that increases on it's own as the bike warms up) is often traced to air leaks in the intake boots. Some guys think spraying stuff on the boots is a definitive test for this, but it's not true. Only gross leaks show up this way.
The valve clearance tightens with mileage, and once all the clearance is gone, the valves hang open and burn. If you wait for your bike to misbehave before performing this critical maintenance, you may damage the engine. If your valves have no clearance you will need a thin "checking shim" in order to achieve some clearance and then calculate the needed shims for your engine.
Checking compression must be done with a warm engine and the throttle held open. If the bike has sat for a long time, you may get a false low reading (Italian tune-up time.) Also, if the valves haven't been adjusted and are hanging open, that will create low compression.
Trying to run the bike without the airbox, or installing pods w/o rejetting, will result in the air/fuel ratio to be drastically lean, which will not only cause running problems, but likely damage the engine by causing it to run hot. Installing a free flowing exhaust will likewise change the jetting requirements, but not as drastically as pods.
"Carb Kits" are often full of inferior aftermarket jets. Typically, the only parts needed during a carb rebuild are fresh O-rings, float bowl gaskets, and maybe float valves. Regarding float valves, consider replacing them if the needle won't hold up the weight of the float, or if the needle is worn. Real deal Mikuni/Keihin parts are best, but Keyster brand is a reasonable option.
Be sure to check your petcock. Fuel should not flow unless vacuum is pulling the diaphragm open when the engine is off. Failed petcocks sometimes send fuel down the vacuum line, so check that too.
If the brake system full of brown gunky fluid, a full system teardown is needed. Flushing won't properly clean the system. Also, the brake lines need to be replaced because there is sure to be brown crud scale on the inside. And even if the system has been maintained, consider changing the rubber brake lines if they are original.
If your charging system fails, install a new stator and (strongly recommended) replace the R/R with a Shindengen SH775 (for those guys running a 3 phase charging system.) The SH775 is a SERIES type R/R, which helps protect your stator from overheat damage from returned excess current. These units almost never fail, and good deals on used units can be found on eBay. BTW, a properly functioning charging system will put out 14-14.5 VDC across the battery at 5k rpm.
Use real motorcycle oil, or diesel engine oil. Don't use car oils, because they don't have as much ZDDP, and they may damage your wet clutch. Some people insist on only using MA (wet clutch) certified oils, which is all well and good, but if you stay with diesel oil you will be fine.