I'll ask the obvious question: is there ANY kind of a gym in your town? A community centre or a college or even a swimming pool? Because although you CAN indeed set up a home gym, you might prefer to simply visit one. Especially when you're new to lifting, it can be helpful to see other people lifting so you can ask people questions when you're not sure how to do a movement.
If this is a "no", then by all means, pick up a cheap bench and some dumbbells. Probably get some 3s, 5s, 8s, 10s, 12s and 15s to start, eventually working your way into picking up a bar (45 pounds) and some plates - but that's later.
Try to get a bench that has an attachment for seated leg extensions.
Eventually, you will need a squat rack, but not right away.
There is a website I send everybody to for information on lifting: http://www.exrx.net/Exercise.html
Ignore their nutrition information, of course, but click on the left to find exercises organised by body part, with little demo movies to show you how to do them.
Have a look for the link at the top of my journal to see what my current routine looks like, but you will probably want to find a routine that does the whole body or a two-day split at first.
Plan to spend 3 or 4 days a week lifting, no longer than an hour a day, and don't do two days in a row if you can help it.
Start with 3 sets of 8 with VERY light weights the first time you do it, just to get form.
For example, a two day split could be:
day 1: stretches (5-10 minutes) and abs (2 minutes)
quads and glutes: squats
back and biceps (look up appropriate exercises)
stretches (5-10 minutes) and abs (2 minutes)
Shoulders chest and triceps (look up appropriate exercises)
When you first do squats, do them with NO weight, and only do two sets of 4. If you can walk the next day, you can increase this to three sets of 5. Work your way up to 3 sets of 10 before holding dumbbells in your hands to do them. Start with the smallest dumbbells, drop back to 3 sets of 5, and work your way back up to 3 sets of 10 before increasing the weight.
A good rule of thumb for most exercises is 3 sets of 8. When you can do 3 sets of 8 and NOT feel it the next day (or not much), you can increase the amount and drop the reps to 3 sets of 5 or 6. Work your way back up to 3 sets of 8, and repeat.
PM me when you've digested the excellent stickies, and when you are ready to start lifting.
Oh, and NEVER do cardio before you lift. Either do it after, or on a separate day.