Litecoin solves the two practical complaints about Bitcoin, speed and fee volatility, and solves none of the privacy question. It is a better version of a public chain rather than a different category.
What it improves
Blocks land roughly every two and a half minutes rather than every ten, so an order funds in ten to fifteen minutes instead of up to an hour. Fees are low and stay low, because the network does not run against a capacity wall the way Bitcoin does during busy periods. For someone who simply wants a public chain payment to land quickly and cheaply, this is the better one.
What it does not change
The ledger. Amount, sending address and receiving address are recorded permanently and readably, exactly as with Bitcoin. Faster and cheaper does not mean more private, and the record produced today will be just as readable in five years.
Where it fits
It is the sensible pick when you have decided a public chain payment is acceptable and you want the practical annoyances removed. It is the wrong pick if you chose it hoping it was quieter than Bitcoin, because it is not.
Wallets
Electrum-LTC is the direct equivalent of the Bitcoin client and behaves the same way. The same rule applies about moving coin off an exchange before spending it.
Verified addresses
anubisqdpukalgiyxlb7rtcya3u6grun2mcozonmb57c54qrt7sqh7qd.onionanubisqe2yramasw5yvlnipaknraza5rzb5uxb7zqhxuxroobvvm6aid.onionanubisqocgruji655mqys7fpafawiy2g56pjqrtecfdikhh5q4zqmfqd.onionBefore you sign in. Open these in Tor Browser only, then compare the onion printed on the login screen against your browser address bar. If they do not match, close the tab.