Home Gym recommendations?

Free weights and a mat.

Free weights, mat and a pull up bar.

A few months ago, I went ahead and bought the "Elite XL" pull up bar from these guys:

http://trapezerigging.com/FreeStandingPortablePullupBar/

I'm 233 pounds, and it supports my weight pretty well as long as I don't make any major swinging / kipping movements. The added benefit is that it can be used for dips, incline push ups, incline pull ups, etc. It's basically the only equipment I need for a full range of bodyweight exercises. Plus, it packs up to about the size of a golf bag, so I can take it on the road with me.

An olympic barbell with plates.
A powercage so you can do whatever you want without a spotter and be safe
An adjustable bench
Floor protection
Cardio equipment of choice
Adjustable dumbbells

And you're all set

Free weights will give you the opportunity to do combination lifts, engaging multiple major muscle groups simultaneously (such as squats). You'll get a better workout and work your stabilizer muscles. Get a free weight set and a dumbbell set (including a mat and a flat or adjustable bench).

Thanks everyone, I am totally new to this so I had to look up most of those terms. Safety is a huge concern since I will be alone most of the time. I am a bit confused my the terms rack vs cage and power vs squat vs free. Are these all basically the same thing?

Sweet looking gym in that picture!

Power Rack, Power Cage, Squat Rack and Squat Cage are all different terms for the same thing. Basically, it's a big contraption with two horizontal bars that can adjust up and down. The idea is that if you fall or drop a weight the bars catch the weights instead of the weights crushing you to a bloody pulp.. Most people find the first option the preferable one If you hop on youtube and search for "squat failure" you can find plenty of examples of people using squat racks, and what can happen if you don't.

Hope that helps. Oh, and thanks

Oh, and you can use the squat rack for more than just squats. You can set the pins so that they'll catch the bar if you fail during a bench press, I do seated overhead presses in there as well for the same reason. Rack pulls need a power rack. A lot of them come with chinup bars as well, and you can get them with bars for doing dips and such too. It's an expensive, but very versatile piece of equipment.

The rubber flooring you have an option. You can buy 4x6' sheets from a gym supply for over $100 a piece, or buy the exact same thing from Tractor Supply Company, sold as horse trailer mats, for $34.99. They're 3/4" thick rubber and stupidly heavy, about 70-80 pounds each. The day you put that in, that is your workout.

This post wins for the most useful info of the day. I have been thinking about getting mats, but all the ones I've seen are way more than I want to spend. Thank you for posting.

Thanks. The one caution if you go that route - you might want to give the mats a quick sniff before you buy them. The ones I got made my basement smell like chicken feed for a week. I didn't mind since it was just my basement, but if you're going to be putting them in a more open area you might want to plan on letting them air out for a few days first.