Sally, the best way to determine which weight to use for your various sets is to find your One Rep Mas (1RM). Now you don't want to go out and start lifting weights that are too heavy for you right off the bat so I'd suggest picking a weight - say 10 lbs and trying that for your chest presses. If it's 'very easy' then you know your 1RM is higher.
Exercises that incorporate many muscle groups will allow you to lift heavier weights (e.g., the chest press, the squat, the deadlift, the skull crusher) than those that isolate muscles (e.g., the fly, the leg extenion, the hamstring curl, the tricep kickback). Lower body exercises will also use higher weights simply because they are larger muscles.
Your set of 6 reps should be approx 80% of your 1RM
Your set of 8 reps should be approx 75% of your 1RM
Your set of 10 reps should be approx 70% of your 1RM
Your set of 12 reps should be approx 65-60% of your 1RM (this is for your initial set of 12, your 'warm up' set).
For your second exercise I would advise going with 75% of your IRM - it's all going to depend on how fatigued your muscles are at this point. As you get stronger this weight will also increase. Remember, this is the exercise where you reach positive failure (the inability to complete another rep with correct form).
As for the free weights - if you're going to work out at home, yes, you might need a few (again, this will depend on the other equipment you own). A weight bench that adjusts to the incline / decline position would be a good investment, as would a curling bar and a good pair of lifting gloves.
If you have any more questions, fire away
Nat