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.
Day trading is a very good job it will give us good income but you need to have trading skills,if you just start the trading without any knowledge then you will lose all the money and your target for a week is very huge and it is hard to achieve even for a professional day traders.So you just start bitcoin trading by doing small trades like upto $100 then if you can find profit from it just carry on with it.
If you are able to invest big amount the you can go for long term bitcoin investment it will give good profit also but it take some years.
Day trading can be very lucrative but also very dangerous if you have not the experience and skills to do it. Start with a low amount, learn everything you can by reading newssites, blogs, forums,... When you are more experienced, than you can invest a bigger amount in bitcoin and altcoins.