Walter, here's some specific ideas.
First of all, you don't have to delete all cookies across all sites necessarily if you are having problems with one web site. (This advice applies only to Firefox and other browsers that have this degree of control - IE does not.)
If you insist on using IE then the following two pieces of advice don't apply. (IE gives you little or no control over these things, at least I cannot find a way to control them.)
In Firefox there is a Options screen menu (Privacy tab, "Show Cookies" button) that allows you to see and work with cookies from all web sites. By entering the domain name in the search box in this window you can search for cookies from only the site having problems. Then, you can select those cookies and remove them.
Secondly, for Firefox there are several add-ons for cookie management. One I use is called "Cookie Monster". It not only makes the process of removing cookies for a particular site very easy, but you can do things like temporarily block cookies for the current site and no other.
Secondly - all cookies, including logins to web sites that you visit, expire periodically. Most news sites expire their cookies after 2 weeks or so. The solution here is to use your browser's "remember" feature to save user names and passwords. So there is kind of a philosophic problem with trying to preserve all of your cookies. You simply can't - they are all temporary (just long lived, but not "that" long) by default.
Lastly, TRexx is absolutely right - cached content can mess up some web sites. Clearing the cache (only) often clears up problems.