So, I decided to open an account at
http://www.treasurydirect.gov/and now I am considering what percentage of my savings should I move there.
What would be the equivalent APY that the treasury bills will yield? Will they compensate for inflation?
TIPS (Treasury Inflation Protected Securities), which are sold by treasurydirect, compensate for inflation. They are a good place to put money that you're pretty sure you will need "soon" -- within the next 5 years or so. Assuming you trust the US government not to default on its debt (I do-- I think the government might try to inflate away the debt, but won't outright default).
Money you won't need soon aught to be invested in something productive-- invest in some business or person that is making our lives more efficient or pleasant. That should give you the best long-term return and will make the world a better place, too. Stock market index funds are an inexpensive, mostly safe, mostly inflation-proof way to invest.
If you have some 'playing around' money that you can afford to lose, you might want to invest in Bitcoins. But bitcoin is a startup currency, and should be treated like a high-tech startup company-- high-risk, but very high potential reward. You might lose your entire investment or it might turn out to be the best investment you ever made.