LTC/BTC and BTC/LTC are both ratios of purchasing one currency with another.
For example, with LTC/BTC, the price quoted is for 1 LTC (overlying) in BTC (underlying). If the price is 0.025, that is how many bitcoins are needed to purchase 1 LTC. At this price, 2 LTC would cost 0.05 BTC.
The opposite would be equivielnt to 1/x, using the example above the rate could also be expressed as 1/0.025, or 40 LTC per bitcoin.
The rate is the same. For some lower valued currency, it would indeed be much better to trade in a BTC/COIN format because it is more likely for an altcoin to go lower than 0.00000001 BTC than to go higher than 100,000,000 BTC per altcoin ;)
For the freshest data, I would recommend going to the source (e.g. a big exchange), such as https://btc-e.com/api/documentation