Training at home is either very limited or very expensive.
A $500 annual gym membership ($50p/month) will typically give you access to A full range of fixed dbs, a lot of weight plates/bbs, lots of benches, machines and classes. That money on a home gym will get you fuck-all weight and maybe a crappy bench. To get a good home gym set up (bb, 200kg of olympic weights, bench, squat rack, pull-up bar, some dbs/kbs) will cost much much more than $500.
If you train at home then the best option is calisthenics (bodyweight exercises) and cardio. Push-ups, air squats, pull-ups, sit-ups, burpees, tricep dips, hand-stand push-ups and running. Local playgrounds can be good value because they have loads of bars for pull-ups and can be combined well with running. A set of gymnastics rings can add an enormous number of possible exercises.
Ultimately though the quickest way to get big and strong is to lift heavy weights, it is not cost-effective to do this at home.