Push ups are not over rated.
An example you can probably see, is Tupac before and after jail. He didnt hit the gym, and he said in interviews that he used to do 300 push ups a day. Hell, we even have his work out regime here somewhere.
Ive seen guys your body type do push ups and sit ups and it DOES help them. I dont think you want to be a big hulk anyway. If you're after it for the looks, definition is sexier than mass, and weights give you MASS.
You could achive a 96 Tupac or Fight Club Brad Pitt body at home with crunches and push ups if you do them properly and only incorporate weights to add resistance to them (put weights on your back or have someone sit on your back).
You dont need weights, Im convinced the whole "you can only get big with weights" has been invented by gyms to get more members. How do you think people in the olden days got big? Gyms? No.
If you want an Arnold / Hulk body, you can only get that at the gym. If you want a toned defined body, you can get that at home.
Weights add mass, but if you have nothing to begin with, you'll get enough mass to look naturally good doing push ups and by the looks of things thats the first step your skinny ass needs to take anyway
Do your home routine, get defined, and then when you reach that and decide you want to go bigger join a gym THEN, but at least then you will have a decent foundation to work off of and you wont burn your arms out after 10 reps and waste your membership fees.