I don't know the exact btc fees but 10$ is a very small budget. You first have to check in which exchange you want to buy the BTC. There will be a fee for buying BTC and perhaps a fee for credit card or something else. When you then transfer the btc to coinexchange you have to pay a fee for transfer. On coinexchange you have to pay a fee for buying. When you transfer the coins to the wallet you also have to pay a fee. So it could be little bit frustrating when you start with 10$ and only get a few coins in your wallet.

So perhaps it would be better to start with for example 50$ if you can.