On the left are screen grabs of the same web site. Take a particular note of the purple message box in the top right of the window when you click on the pictures to see them expanded.
The purple message box was written to have rounded corners, a shadow and a graduated blend of colours from top to bottom.
Internet Explorer is a web designers nightmare as it does not conform to the international web coding standards and we have to add extra code to get the site working something like it.
If you look at the first picture (Internet Explorer) you can see that it doesn't show rounded corners, shadows or colour gradients.
The second picture is from Opera. It can render corners and shadows but not gradients.
The third picture is from Safari and it renders corners, shadows and gradients fine. Google's browser (Chrome) and Firefox are almost identical to Safari in how they render a page.
Personally, I believe Safari, Chrome and Firefox shows the web site closest to the way I built it and I would recommend that you use one of those three browsers.
IMHO:
If you have a Windows PC then Chrome or Firefox are probably the best browsers to use.
If you have an Apple Mac then Safari or Chrome are probably best for you.
At the end of the day it is your choice which browser you use, but if you think my web sites look good in Internet Explorer wait until you see what they look like in Firefox, Chrome or Safari.