first what do i copy over to get my account, gamesaves and the games over to the hard drive and can i use this back up from my external hard drive to recover everything if my computer breaks and get a new one
Saves.
As long as the game has steam cloud support, the saves are there and will just sync with your account on whatever computer you log into. If you want to back them up manually, then you'll have to look it up for each game, as there is no standard place for saves (some games will put them in documents folder, other games will keep them in the same folder as the game).
Account.
There's nothing to back up. If you install steam on another computer, you just log in with your username/password the same as you do any other service.
Games.
You can either use the steam backup option. Properties on whatever game you want to back up, then local files, then backup game files. This takes a while, but gives you a single file. If you don't want to use the backup option, you can just copy the games folder from steamapps/common and also the games .acf from steamapps, without the .acf steam won't show the game as installed. You can find the right .acf by looking on the steam store and looking at the url for the game, which will have app/number. Then look for same numbered .acf. This is quicker than using the backup option.
Or if you have a fast connection, just don't bother. If you move pc/your hdd breaks, just log in to steam and redownload your games.