Ok, first, the reason the new css class probably didn't work is because those are links you are trying to format, so they are defaulting to the a:link class. If you want to format links, you need to add not one, but 4 new classes. For example, if you wanted a new class called 'minicart' you would need to create:
.minicart: link
.minicart: hover
.minicart: visited
.minicart: active
Next, the reason your buttons have borders is because they are linked
If you want to remove the border, you need to add this to each of your images:
border="0"
So the checkout button code would look like this:
[img]skin1/images/checkout_p.gif[/img]
Finally, you should call your images using smarty so that you don't get any missing images or secure server problems down the road. Again using the checkout button as an example would be called like this:
[img]{$ImagesDir}/checkout_p.gif[/img]
Just make sure you put all of your images in skin1/images.
Hope this helps!