Given that I already have a desktop, and with the investment of < 500$ for GPUs, what is the best hardware to mine litecoins?
You would probably want to invest in 1 AMD Radeon card, for example 280x or 290. This is private opinion based, but AMD seems to provide good hash rate for money. Have a look at litecoin hardware comparison site for the estimated hash rate.
Is it worth mining litecoins with such hardware?
If you can get around 750 KH/s, this would yield around $130 over 30 days (source). Note the price is fluctuating a lot, so by no means this is set in stone.
Are ASICs available for litecoin mining?
No, there aren't at the moment. It takes time to develop and test custom circuit. Not advertising here, but this company appears to offer two models: 5 MH/s (£1350) and 25 MH/s (£5450) with the release date due in Q2-Q3 2014. It's up to you if you would trust them and pay a deposit. Obviously, there will be many others cooking similar stuff in the next half a year (Q1-Q2 2014).