I agree with Debinmi's feedback. Here is mine: Dumbbells are an absolute must, everything else could be modified. But what you have is absolutely fine in my opinion.
*Dumbbells (mine are 3-52 lbs)
*Barbell (Cathe always shows someone using DBs instead of a BB, so not required) (I believe I use up to 100 lbs)
*Bench (can use a step or even the floor or a stability ball) (some exercises are done at an incline, but you could do them flat)
*Stability Ball - you could substitute a bench, floor or step. A ball is nice because you do get the incline and she does a few exercises with the ball as decline push ups or incline push ups (elmo-style)....but could be subbed with above.
*Weighted Vest (mine is 20 lbs....any heavier and it compresses my breasts too much!) (This is really only needed if you do the squat rack DVD and if you just can't lift a heavy enough barbell over your head and need the extra weight in the vest) (If there was something you were to add, I would add this if you are doing the Squat Rack DVDs.)
*Weighted gloves (Mine are 1-2lbs) (not necessary, but it really helps add strength because sometimes you just can't go up a full 5 lbs in dumbbells) (In a couple of exercises, Cathe uses just the gloves....you can use 2-3 lb dumbbells instead)
*Fit Tower - Cathe does do pull ups & Chin Ups. There are options to use tubing attached to a door, but I get better results from a tower versus the tubing. Look up Mark Lauren from "You are your own Body" on how to use household furniture as a pull-up apparatus. (this would be the 2nd item I would add to your collection after a weighted vest if you have the room and means)
*Gliding disks (could use paper plates or rags or "moving men")
*Bands - could always use a dumbbell and modify an exercise, but bands are so versatile and inexpensive, I would recommend them.
*Tubing - could modify with bands and vice versa.
*Firewalker loops - could substitute with a tied up band
*High Step - I believe Cathe uses up to 4 risers. You could always substitute with a chair or sturdy box.
*Barbell Pad for neck - not necessary, but does make it more comfortable (you could use a towel as a pad)
*Workout gloves - not necessary, but does make it more comfortable.
*Ankle Weights - I have 2-7.5 lbs each. Not necessary as you could lay a dumbbell on your leg or use a firewalker loop. Plus, there are such few exercises ankle weights are used.
I think you are set for STS with what you have right now! If anything, you can do it once and see what you would like to add for future STS rotations.