Charly, a few things to add to the good suggestions you got above.
First, I take the same gear with me when I go on day rides as when I go on a 6 week trip. Really, there is no difference between getting stuck 300 miles from home to being stuck 3000 miles from home. You always have to have some basics:
Tire repair kit - cheap string-type kits work surprisingly well, take less space in your bags. After carrying all sort of "sophisticated" alternatives, I am back to the ~$5 ($8 if you want to splurge on a kit that has T handles
) string-type kits. As mentioned above, have some experience using it in the comfort of your own home is invaluable. I carry a small, high capacity, manual pump and now also a Slime electrical one. In reality, now that I have the Slime pump I don't really need to the hand-pump, but since it takes virtually no space, it's a useful backup.
Tools - Get familiar with your bike and what tools are required for basic maintenance. How do you take a wheel off? How to remove the fairing to get to the coolant reservoir, headlights, etc? Know how to do those things and what tools are needed. Make sure you take those with you on those trips (don't count on the Kawasaki tool kit, it's just a paperweight for most things, but you can take some useful tools out of it, or replace the not-so-useful ones with a better tool).
Riding gear - Where will you be riding? I don't remember where you live, but out here in the PNWet, you can leave your house in nice comfy temps and by the time you covered the first 80 miles be freezing across some mountain pass. Plan for the different weather conditions you'll find along the way, always assume the worst condition in the forecast will happen, not the other way around. Remember, you are not in a car, if it's 50 deg up on the mountain passes, it will feel even colder with wind chill. If you plan to ride in cold temps, consider electric gear, there is nothing that works better to keep you warm.
There are lots of options for bags, but having a lockable hard bag (be it a top case or side cases) makes your life easier when touring. It's relatively secure, keeps honest people honest (but obviously is not 100% secure, if someone wants what's in it badly enough, they'll get it, just like your car) and keeps your stuff dry (at least Givi bags do) To reduce the initial cost, I usually buy a top case and if I really need more capacity I use a pair of soft saddlebags for those trips. I can go on a 2 week trip (in summer) with just a tank bag and a top case.
Which brings me to the next related topic, packing. Pack light. It's going to be hard on your first overnight trips, but in most cases half the "stuff" you take with you is never used. If it doesn't fall into the tools/tire repair category (stuff you may carry around for years without using, but wouldn't leave behind) leave it at home next time. My wife and I rode for 6 weeks around Mexico and did it with one pair of soft saddlebags, tank-bag and a top case.
Here is my setup for a 6 day, ~4000 mile trip:
Hope this helps,