Bodyweight exercise has been a staple of my training, and I have indeed put on 40 lbs. of muscle in these past 10 months, as a newbie, without a gym membership. The key is to train smart and to eat smart:
Progressively more difficult exercises, knowing when to back off for rest, and progressively better dietary choices and timing.
You will want to invest at least in a chin-up bar, for $20. You may also invest in dumbbells, buying one pair at a time. Actually, you'll want to get two pair to start, as a light pair is necessary for warm-up or for training the very small muscle groups (like deltoid isolation).
A barbell set would be a nice investment as well, though more of an initial pay-out. You can find equipment somewhat cheaper at a second-hand sports store.
Train the compound movements first. Here is weightlifting in a nutshell, the prime six movements:
Horizontal Press (push-up, bench press)
Horziontal Pull (inverse row, bent row)
Vertical Press (handstand push-up, military press)
Vertical Pull (pull-up, pull-down machine)
Quad Dominant (bodyweight squats, squats)
Hip Dominant (bodyweight deadlift, deadlift)
Since bodyweight squats and deadlifts are not very challenging, try them on one leg at a time. This will also help to even out any imbalances between legs.
If you are unable to perform any of the bodyweight movements - such as handstand push-ups - you can progress with feet elevated push-ups, gradually increasing the elevation. Same with pull-ups, going from an inverse row to something more upright and with feet not touching the ground. For one-legged squats, you can begin by starting in the down position, and standing up.
It's possible to get "big enough" and "strong enough" without a gym membership or even much of a home gym. Last week was a breakthrough for me, as while wearing loose fitting clothing, some strangers commented that I must lift weights. My biggest dumbbells are only 35 lbs. But I can do 16 handstand push-ups and 8 one-legged squats while holding that dumbbell.
Lol @ gym weenies that can't put up. If you have a brain, gym membership is not essential, not even close. Good luck!