So if I were to designs the shirts, would it be ok to put that copyright thing on it down in the corner or something, or would i have to file a copyright with the government to do that?
You can use the circle c copyright mark without officially registering your work with the government.
Officially registering it with the government helps you prove you created the work first and helps you collect damages if you wanted to take someone to court.
I haven't actually designed the shirts yet, I've just wrote the sayings.
You generally can't copyright or trademark a "saying", although there are some exceptions (like when the saying is a part of brand...like "Just Do It"). You can read more on the copyright and trademark websites.
Another thing, if I were to become a freelancer, and I were to show people my work, would they be able to steal it since i haven't copyrighted with the government or is that automatic copyright good enough?
One way to think about it is that someone can
always steal your work. You can't really stop someone from the
actual act of stealing it. Sometimes it's unintentional (coincidence of coming up with the same design as someone else).
Think of copyrights and trademarks as "after the fact" protection.
Yes, registering them can help deter someone from taking it if they do the research to find out if the it's already been registered.
I'm not a lawyer, but personally I think the real benefit to an official trademark/copyright registration is what protection you have "after" you find someone has used your design.
That registration gives you official proof that you created the design first, came up with the brand first. This can help you get the person using your design to stop and puts the law on your side.