I personaly prefer e-Gold of National Spot Exchange (More Info - http://www.nationalspotexchange.com/eseries.htm?m=3)
Charges I have no idea, please check NSE for this info. Both you buy and store in your demat.
Gold Mutual Fund
It is a MF which invests in gold. In simple words - When you buy in a gold mutual fund, the fund managers invest your money in gold.
GOLD Exchange Traded Fund
Gold ETF - which can be bought and sold in the stock market like any other shares or equities.

More Info -
http://www.investopedia.com/ask/answ...l-fund-etf.asp