There are two keys to working with back/joint problems: 1. Form and Control are Critical; 2. Listen to your body very carefully.
I have a LOT of spine and joint problems I was born with. The only way I've NEVER hurt myself is lifting weights (I've put my back out putting on shoes, using the bathroom, taking a shower, you get the picture).
You have to figure out what movements you can do WITHOUT causing pain when you aren't lifting weights, first. For example, if you know that bending over to tie your shoe causes pain, forget doing a similar movement with weight.
Generally speaking, with lower back problems you really want to avoid high impact stuff (things like running, trampoline, impact sports are all out). Running is one of the worst things you can do if you have a bad back, BTW, even on a treadmill. Walking and aquatic work, biking and elliptical trainer. Stay away from ANYTHING that looks like a stepper machine.
Finally, form and core strength are critical. Forget floor crunches, they're awful if you have back problems. Also, you probably should avoid hyperextension of the back (like reverse sit ups). Weighted situps are also in that category. Hanging leg lifts are very good, first, you're hanging, which is good for your back, second, they truly exercise the core versus a lot of other so called "ab" workouts. However, don't try to get fancy and add any twisting with them. You just want to raise your knees to your chest. I also can do seated cable crunches. Again, form and listen to your body.
Always start out working light, and if something causes pain, drop the weight and up the reps. Listen to your body. I do deadlifts but I know what my limit is. I have to work lighter than I'd like because too heavy puts the wrong stress on my back. I make up for it by adding reps.