I personally needed a gym membership to get my motivation. I have nearly everything I need for a real good workout in my basement. But I simply could not get myself to go down there. And when I would, I would just get distracted and have very unproductive workouts.
One day I got changed to go workout in the basement, sat on the couch for 5 seconds. My friend had the TV on, and next thing I knew it was 25 minutes later and I didn't have time for a full workout. I got pissed at myself, stood up, and drove to the gym to sign up right then. Best decision I've ever made. Since joining a couple months back, I now hit the gym 4-5 times per week. What helped me even more was getting a trainer once a week. I signed up for 12 sessions with him, and he has helped me put workouts together tailored to my wants/needs. Now, I feel like I go to the gym for a purpose. Not to just throw a bunch of exercises together hoping to get in shape.
Plus, as far as dumbbells go(and maybe plates), it sounds like you are very limited. You could outgrow those in 2 weeks. Then what? If you can find the motivation at home, it sounds like you will need to make some purchases. But if you ask me, joining a gym is the best solution.
I've made some friends there, get motivation seeing other people lifting more than me, and some of the girls are nice to look at
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