I belonged to a health club for about a year. I miss the pool. Well, that and the whirlpool and sauna. Otherwise, it's a waste of money if all you want to do is get and stay in shape. If you're there for social reasons, then you're not going to like my workout routine. If, on the other hand, you're looking for an economical solution to get in the fitness habit then read on.
Fitness habit, that's important. You need to get in the habit of working out and once you do you've won the battle.
All you have to do is set a specific time of day you want to do your workout. I like doing mine first thing in the morning, around 6am. There's theories that it's best to do physical fitness in the morning as opposed to at the end of the day but I'm not going to get into that. It's more important that you choose a time you like and stick to it.
Sticking to it is the other part of the success formula. Adhere to your workout schedule, mine is six times a week, for three months. It'll be a tough 90 days or so. There will be times when the last thing you want to do is workout. Fight through that and just do it.
After doing something that's good for you, routinely, for three months you're going to start feeling guilty when you skip a day. There'll still be days you don't feel like it but you'll feel worse if you skip it. It'll nag on your mind throughout the day. And that's a good thing. It forces you to do the workout. Besides, in the end you feel and look better.
Break down your workout regimen into two parts, aerobics and weight training. Alternate days between the two forms of exercise.
I'm a bike rider. I have always loved riding my bike. I'm not one of those hard-core, speed freak riders that's prepping for the Tour De France. I get by just fine with a steady clip, enjoying the ride on the all-purpose trail as opposed to the road. I'm fortunate to have the Cleveland Metroparks close by, and there's nothing that will raise your heart rate better than a pedal through the park and a deer running across your path just a bit too close. My three times a week morning bike ride lasts an hour. Though on Sundays I may ride for much longer because it's hardly work. I love my bike.
When the cold weather hits I either ride my stationary bike or use one of those adjustable exercise steps, alternating legs every 10 minutes. Either way, I spend an hour on the routine.

As for the weight training you can get by on a couple of pairs of dumbbells at different weights and a dumbbell bench, the kind without the arms you'd use with barbells. Something as simple as this. 
I use those solid weights so you don't have to mess around with adding or removing weights.
On Mondays I have a weight routine in which I concentrate on my lower body while on Wednesdays and Fridays I focus on the upper body. There's plenty of sources to find a good variety of specific exercises to do. Just find a good group of them and make that your routine.
I use a notebook to write down each exercise then daily jot down how many reps I did. I have pages and pages of numbers which give physical proof to my commitment and work as a good motivator.
In weight training the rule of thumb is three sets of a certain number of reps that increase as you stay true to your fitness routine. There's other advise on weight training like doing it slowly and steadily. You'll find that sort of guidance when you look for those dumbbell exercises online.
Finally I use one of those exercise wheels both on weight and aerobic days. I hate sit ups and this stalwart is very effective in tightening up your stomach and getting rid of that gut.

Weight training days are a bit shorter, maybe 45 minutes or so. Of course, if you're just starting out your routine will be shorter than mine but will gradually lengthen as will the poundage of the weights and the distance of the ride. At this point I'll recommend you run the fitness routine by your doctor. For goodness sakes, if you're over 40 and don't see your doctor annually you'd better change that. Preventive maintenance is so important.
So let's see, there's the outdoor bike, the stationary bike, the exercise step, weights and a bench. And if you're lucky enough that your body can take the pounding of running, mine can't, then you don't need the bikes. It's much cheaper than the annual dues at a fitness club and you don't need all that complex machinery in your home either. The important thing is the results and I guarantee they are the same with this economic routine.