Welcome Jenaya
Well, personally I prefer free weights *over* machines, if I had to choose between the two; but I do like having access to both. If you're going to work out at home, you will probably need to keep buying weights as you become stronger - or invest in a set of PowerBlocks or other type of adjustable dumbbell.
The machines I use regularly at my gym are:
Calf raise machines (seated and standing)
Leg Extension
Leg Curl (lying and seated)
Leg Press
Dip machine
Pec Deck
Cable station for seated rows, tri pressdowns, pulldowns, cable curls, etc.
You might try getting a trial membership to your local gym before you 'invest' so you can decide what would work best for you. I love my gym