BTC e (one of the big cryptocurrency exchanges) support direct LTC to USD exchanges. They don't seem to facilitate FTC to USD directly (gotta go through bitcoins), but it would not surprise me if somebody else does.
 

Mt. Gox is the biggest cryptocurrency exchange, and they might support it. They've gotten some bad press lately, but a lot of people still prefer them.

Good luck!

I've heard some people say litecoins are the most profitable at the moment. Any thoughts on whether or not that's true?

No, I'm pretty sure they're just a BTC wallet. You can send funds from there to BTC e or Mt. Gox to trade for alt coins, though.

Does anyone know what the process is like for putting USD into localbitcoin escrow? Like, is a lot of banking information required? Does verification take a long time? Is it better just to trade in person with cash?

I read about it on their website, but it was kind of vague....   

I'm new to bitcoin, but based on what I know of economics at large, it all comes back to supply and demand. The supply is running out fast, in the sense that mining seems to become less and less cost effective (I've been told). The demand is the big question mark.
I would argue that the value of bitcoin is mostly speculative. People are interested in it either because they think it's going to catch on as a major currency (where it's actually practical to buy stuff with it), or they expect to be able to trade it for more fiat currency than they paid for it (an investment).

All major currencies today, and indeed corprate stocks as well, are built on percieved value. I can go to a store a trade a $5 bill for a roll of toilet paper, because me and the business and the girl at the checkout counter all agree to "pretend" that that green slip of paper is worth something.

A bubble pops when enough people (or a few wealthy people) stop believing the given commodity is worth as much as has been previously accepted. They cash out, and the value tanks. In the late 1920s the US stock market crashed because enough people realized the prices were artificially inflated far above their actual value. Same with the .COM bubble of the 90s, and the housing market crash just a few years ago.

The thing that makes Bitcoins a little harder to predict, is that their value isn't really tied to any real world object (IE- the value of a single company, as with stocks). It's speculative. It based on an assumption that other people will accept that a coin is worth more than we paid, just as we accepted it's worth more than our bitcoin forefathers paid. Or else that the market stabalizes and it becomes a practical online currency. (The big picture idealists.)