Which cryptocurrencies are better suited to users with limited bandwidth?
Apart from a few cryptocurrencies, including Bitcoin, most of them have very low exchange rates. So although you will find many such virtual currencies, it won't be profitable either way. And mining does not require bandwidth as such, it's only the blockchain synchronization which would be slower with a lower bandwidth. Mining is achieved by your machine and not the bandwidth.

If it's only the knowledge you wish to gain, then you can use the bitcoin testnet to mine test bitcoins, however trading testnet coins is not an option.