What is the minimum cost for alpha access?

Star Citizen has a link on their homepage that says "Reserve Your Alpha Slot." However, clicking it simply takes you to their store's main page, which has no information regarding which purchases grant you access to the alpha. The only information regarding the alpha that I can find is that the Aurora MR "does not include access to the Alpha and Beta of the game."

Does this mean that all other purchases do? Also, if one makes a purchase that grants access to the alpha, does this also grant them access to the game once it's released, or will that cost extra?

When you are at the pledge store, look under the "Game Packages" section on the left of the page. Under that you should see "Single Ship Packages." Any of those will have alpha and beta access as well as the game. If you click on the "more info" under the packages, it tells you exactly what you get with it. You should see "Alpha Access" and "Beta Access" down at the bottom of the page in the "Also Contains" section under "This Package Contains:"

For example, taken from the Aurora LN page: