You don't say what version of Eraser you are using, though the general principles are the same for both v5 and v6.
To make things simple, I shall assume that
- your data is not of interest to such well-equipped organisations as your country's security authorities, so that the intent is to make the data impossible to recover for the great majority of people who might want to see it, and not worth the effort of recovery for the technically sophisticated remainder;
- the drive is not the system drive from which you are running Windows and Eraser.
In general, the more passes the method requires, the slower it will be. And, when you are talking about a 1TB drive, no method will actually be fast; erasing free space on a drive of that size will take many hours, certainly overnight, perhaps a full day, even with the default single pass pseudo-random data method, which is probably the fastest. This is a function of drive technology, rather than of Eraser.
While this is running, you could consider disconnecting your computer from your network/the Internet, and temporarily disabling your security programs and anything else (except Eraser!) that runs in the background. Eraser will want to monopolise the hard drive and will compete with running programs for system resources; it is as well to let it run as freely as possible.
In your circumstances, I would tend to use a 3 pass method for the actual data on the drive; being a Brit, I use the HMG IS5 (Enhanced) method for my data erasing. I would then use the one pass pseudo-random method for the free space. And I'd (quick) format the drive to clear the FAT. For 99.99%+ of people, that should be enough to make the data on the drive safely inaccessible. But don't do it until you don't need the computer for anything else for a while.
Hope this helps,