There are a few things you should do when you have bought a secondhand motorcycle.
Probably one of the important checks you should do after you bought your used motorcycle is check the bearings. That's steering head, swingarm pivot, suspension linkage and both wheels. But especially the head bearing: the slightest deterioration will make your motorcycle feel like an old lady. Support the front of the motorcycle on a beam across two axle stands and drift the old races out. To fish the tight bottom race off the steering stem, carefully grind the race off with a bench grinder. Fresh bearings now come with new rubber seals. You will be amazed how easy it is now-a-day to find new bearings for anything on your motorcycle.
Look with a critical eye at your tires, are they in the right size, are they fitted correctly, recommended for the motorcycle? Sound obvious, but it often isn't. The reason to shell out some money on new tires is because they make your motorcycle feel great every time it turns a wheel. The latest generation of sports touring tires from any of the big names are more than adequate for nearly everyone and every machine, even if you do the odd trackday. You should also check the controls. Remove, clean and lubricate the brake and clutch leers. Use decent quality lithium grease on the pivots and silicone grease on the ram actuating surfaces. Repeat for the rear. Set both foot and both hand controls at an angle and span the suits you. Lubricate the clutch and throttle cables, using the right lubrication for whatever cable type you have. Why bother with all this? To remove the tiny snags that interfere with your control. Sure, they are only tiny – but they are there all the time until you tweak the motorcycle to suit you.
Check your suspension. If the motorcycle is three or more years old, you should serious consider rebuilding the forks, and look around for aftermarket rear shock or shocks. If you rebuild your front forks you can select the correct springs for your weight and riding style. If this all is out of you budget, you should at least set the preload properly for your weight. You also change fork oil regularly too. Drain the old out (via the drain plug on the fork leg) and replace with the recommended oil. Remove the fork caps, but be careful as the springs is under pressure and can fire out of the top of the fork leg. Take all load off the front of the motorcycle