Stick the the big lifts mate (Squat, Deadlift, Bench & Military Press). Look up Mark Rippertoe - Starting Strength to get a workout plan and how to do the exercises correctly. 5x5 is also a decent beginners program.

You'l need a bar, bench and something to act like a squat rack. The 80kg weights you have will be plenty for while your starting out.

I'm no Doctor or Physio but maybe the weight machines gave you a problem because they tend to isolate muscle groups. If your weak in a particular area I can see how they might isolate the problem and exacerbate it. When you join a gym pick one that has good free weights facilities.

Free weights will work your stabiliser muscles which are the small supporting muscles surrounding the major ones. This will in turn make you much stronger and may help with your injuries as the supporting muscles will be strengthened.

If this is something you go ahead with then please remember the most important thing is to learn how to do the exercises correctly. Have someone teach you and make them watch your form before going it alone. Also start ridiculously light and work your way up.