I actually do go to the gym since it's free for me (one of the perks of being married to an academic), and I often workout outdoors. I do however recognize that it's still useful to have some equipment at home for working out. Here's what I came up with:
- Jump rope - a $5 speed rope is sufficient for a fabulous cardio workout that will work your legs, core, and arms. If you want to splurge, you can get a $40 Buddy Lee Aero Speed.
- Gymnastics rings or suspension trainer - I'm a big fan of bodyweight resistance training. A TRX trainer is a pretty versatile piece of training equipment that you can use to hit basically every part of your body. You can also go the DIY route if you don't want to spring the cash to buy the commercial product. Gymnastics rings (like Elite Rings or Xtreme Rings) are similarly fantastic total upper body workout.
- Resistance bands or tubing - Elastic bands and tubing are really versatile and just as challenging as weights once you get bands/tubes thick enough. I have trouble even opening my 2.25" inch band. As an added bonus, they take up far less space than regular weights.
- Pull up bar - You could technically get by with just some rings or a suspension trainer, but if you opt not to get one of those, you need at least something to pull yourself up on. There are plenty of DIY solutions for this, though commercial products are certainly a viable option.
- Foam roller - Keeping your soft tissue healthy is an important part of your training! Tennis balls, lacrosse balls, rolling pins, wood dowels are also acceptable substitutes and complements to the foam roller for maintaining your soft tissue health.
Nice to have
- Dumbbells - Weights with handles. They're basic, can be used in many exercises, and can usually be picked up used for pretty cheap. If you want to go fancy, you can even get adjustable weight dumbbells.
- Kettlebells - Once you know what you're doing, kettlebells are a great training tool for strength and conditioning. I wouldn't prioritize getting bells like some of the kettlebell fanboys, but they are admittedly versatile and worthy of adding to your fitness gear collection.
- Medicine balls - Do twists, slams, throws, or just use them as a weight.
- Sledgehammer - Just go the hardware store and pick up a sledgehammer. Find an old tire. Swing at the tire for rounds and intervals until tired. You'll be thoroughly de-stressed and be building a physique with explosive power. Pair the sledgehammer swings (anterior chain) with kettlebell swings (posterior chain), and you have a pretty complete strength and conditioning workout.
- Swiss ball (or stability/physio/body/fitness ball) - This isn't a strictly necessary piece of equipment, but it's cheap enough and versatile enough to make it worthwhile. Sometimes you just need to make an exercise slightly unstable to improve your strength levels.
- Sandbags, Bulgarian bag (or other odd object weight) - You can easily make these yourself. The non-rigid nature of the bags adds a stability challenge and makes for an effective workout.
Only if you have room and/or discretionary funds
- Erg / Rowing machine - Rowing is a great cardio workout that hits the upper and lower body. The machines can be a bit pricey, but can be worth it if you're dead set on working out primarily at home.
- Barbell with weights - Again, weights and a handle are pretty basic, but simplicity trumps fancy training in my opinion. I prioritize dumbbells over the barbell since I think dumbbells are more versatile overall.
- Power/Squat Rack - If you want to be seriously strong, you'll need to train your legs and squat. You'll probably want some measure of safety when holding heavy weights on your shoulders. As an added bonus, you normally get a pull up bar in a rack. Personally, I prefer going to the gym for the squat racks.
- Bench - I like a padded elevated surface for certain exercises. Dragon flags with my shoulders on a hard surface are no fun.
- Heavy Bag - Getting my heart rate up while training full body mechanics and hitting something is incredibly fun. I'm always in a better mood after yelling obscenities and pounding the bag. Ok, scratch the yelling obscenities part, but I do feel better from hitting the bag.
I realize my list is highly biased to my own training. I'm partial to bodyweight training, resistance strength training, and interval cardio training. I also really like exercises which I believe have good functional carryover to other activities, which means my equipment choices favor compound and stabilization movements.
I intentionally left the typical cardio machines off the list (treadmill, elliptical, bike), because I think they just aren't necessary. The treadmill and elliptical in particular I don't like. They're expensive to buy decent ones, and have serious shortcomings that preclude them from being regular training tools in my view. Treadmills move your foot back for you and basically give your hamstrings and glutes a free pass during your running. This leads to an imbalance between the quads and hamstrings/glutes. That's a recipe for future knee pain if you do the treadmill all the time. Elliptical trainers tend to put the pelvis in posterior tilt, which is not a postural habit you want ingrained. Modern sedentary life (i.e. sitting desk jobs, sitting in cars, couch lounging, etc) already puts a lot of us in posterior pelvic tilt. Reinforcing that posture during your regular cardio workout is not doing your spine a favor.
I also left off the typical "universal" weight machine you see in a lot of home gyms. They are far too expensive and generally provide sucky versions of all the exercises at each of the stations. Quite frankly, you're better off with either dumbbells and a bench, or a pull up bar and just open floor space.
Anyhow, that's my take on equipping a home gym. I'm sure I left some things off the list, but I think the list is a good launching point.