Assuming I can gather 500$ a week from here and there,how much exactly should I invest.
I'm not that greedy and there is no time constraint.
500$ is not a huge amount to start big deals in trading world. But if you can earning this amount weekly and investing at least its half or a bit less in Bitcoin and the other amount in promising altcoins and ICO's projects, I think you will get some profit.
Agreed! The current price if bitcoin is 12k$ which means that investing this much of money will not even help you in getting 0.5 bitcoin. It all depends on your income as well as the amount of money you do have in your account. If you are really interested in investing your money into bitcoin, then you need to invest somewhat around 60-70% of your total income. This will help you in having more profit in return.