To what extent do your choices in Mass Effect influence the story in Mass Effect 2?

I am about to start the first game and would like to know how much Mass Effect 2 relies on choices made in the first game.

Is the story rather set in stone and just little things are influenced, or can the story across the first two games change drastically depending on your choices?

Solution 1:

There are many small carry over effects from ME1->ME2, but here are the major ones:

1. Depending on who you save on Virmire, that person will make an appearance in ME2 and be a squad member in ME3 (Your love interest may carry over as well, assuming you didn't cheat on them in ME2).
2. If Wrex dies in ME1, then the state of the Krogans will be different in ME2.
3. Depending on whether or not you saved the council, the rest of the races in galaxy may be bitter towards the humans.

Since ME3 is not out yet, there's no way to know what decisions from ME1 and ME2 affect the story in ME3.

Solution 2:

The Mass Effect Wiki has a nice page about what transfers.. A lot of the decisions that transfer happen at the end of the game and are very obvious they transfer.