Steam – I deleted steamapps to uninstall steam can i get the games back though

Yes, games linked to your Steam account can be installed / uninstalled at will.

There are some rare exceptions where a game has additional DRM that limits the number of times you can install - but this should always be noted on the game's store page (the first example I've found is Dead Space 2, check the wall of capitalised text carefully to see what I mean) and there is often a way to "reclaim" those installs before you uninstall the game. So check the Store page for each game before you uninstall if this is a concern.

When you want to reinstall:
On your game list, if you switch to the "All Games" view you will find all the games you have linked to your account. Those that are not currently installed will be greyed out, and from here you can select for them to be downloaded and installed.

I know this is an old question, but for future generations:

Copy Steam_directory/userdata/your_long_number/7/remote/sharedconfig.vdf between computers or back it up.

Steam_directory is~/.local/share/Steam/ on linux, ~/Library/Application Support/Steam on mac, and wherever you chose to install Steam on windows (usually C:\Program Files\Steam or C:\Program Files (x86)\Steam).