What are the best dimensions for website home page?

The dimensions will be based on your audience. If you can gather these statistics yourself, that is a better idea, but you can also get the general statistics from the link below.

At the time of this writing, almost half of all Internet users have a screen resolution of 1024x768. Use a width less than 980 pixels. This will keep your users from having to scroll horizontally to see remaining text.

A significant number of users have an 800x600 resolution. Use a width less than 760 pixels.

For print, use a width less than 560 pixels. To accommodate printing and a wider screen resolutions, use the media attribute of the CSS <link> tag.

No users in this statistic use a screen resolution lower than 800x600, but a significant number of a users have a screen resolution higher than 1024x768. Since you will never be able to satisfy all users across platforms, it is better to use relative positioning - aka fluid websites - for scalability. But if you want to reach only one type of user, then static positioning - aka fixed widths - is the way to go. You should weigh the pros and cons of each based on your goals and purpose.