The benefit of using the default list forms is that they have the attachment logic built in. I often rearrange things on the default forms simply by using script to manipulate the DOM elements and CSS. You can do this without SharePoint Designer, though it certainly is easier if you use it.
There's an Add Attachment operation in the Lists Web Services if you'd rather go that route. You'll have to build your own way for the user to browse to or otherwise identify the file.
M.