There seems to be several potential issues rolled into one here. Lets start with cookies. As previously said these are just small text files and in themselves cannot run anythin malicious on your PC. There are 2 kinds of cookies: Session cookies which will be used on most sites even this one. These cookies are just remembered in your web browser and are used to remember personal settings such as language etc so that these are carried onto other pages on the website as you surf. These cookies disappear when you close your web browser. The second type of cookies are known as persistent cookies. These are saved to your hard disk. These cookies are used to remember you if you come back to visit the site at a later date. You may notice that some sites allow you to select for the site to remember you next time you visit. It will populate your user name and password automatically. It can do this because of the persistent cookie it sent you first time. All cookies can be removed easily and after a while it is worth clearing them out. A good free product for this is CCleaner which will also clean up temp files and caches.Its free to download and use. Other pop up messages that you can get from some sites revolve around active x which is a programming method that means certain functions on a web site can act independently of the programming language used to write the website. A lot of sites are now using this and very often your internet security software will flag this as a risk. Pop up and banner ads that "pop up" when you go to a web site are generally annoying but easy to block either through your internet security software or in your browser. As a final point, it is right that you should be concerned about online safety and security, but as a general rule if you have good anti virus and internet security software and keep it up to date you should be safe.
Don't worry too much about cookies, they just allow a site to see if you're visiting again and what your browsing habits are. Just don't install any proposed SW or accept other things proposed by the site itself
In Firefox you can choose cookie options by clicking "tools" on the menu bar, then selecting "options" and choosing the "privacy" tab. Cookies are easily deleted when you are finished using the internet. You can also control cookies on IE by clicking on "tools" and choosing "internet options". I normally only get warnings about running Active X add-ons-such as Adobe Flash or Shockwave. These are needed to play games and to use some websites.