You've already received good information. I write only to put a fine point on a fact that my colleagues have mentioned: just because a phrase is slapped on a product does NOT mean the phrase serves as a trademark.
A trademark serves to identify the SOURCE of the product -- not the product itself.
For example, when a consumer sees the Nike Swoosh on a product the consumer knows the source of that product is Nike. The Swoosh does not convey any information to the consumer about that particular product [it cannot because it's affixed to many different products] other than that Nike stands behind that product [by either making it or having it made].
But if a consumer sees the phrase "Have a Nice Day" on a product the consumer does NOT know the source of the product because that phrase is not associated with any ONE particular company. "Have a Nice Day" cannot be a trademark [unless, as my colleagues mentioned, an enormous amount of advertising and other marketing efforts create in the consumer's minds an association between that phrase and ONE company]. The phrase is not copyrightable either because short phrases are, as a general rule, not copyrightable. So ANYONE can lawfully slap "Have a Nice Day" on the same products that you do and both of you would have compete for customers. Which is a good thing. There are, as you can imagine, many such unprotectable phrases.
Most "designs" are copyrightable. Some simple ones are not. Copyrightable designs that are made to be displayed along with a phrase are also copyrightable. The copyright prevents anyone from reproducing or distributing the design -- either in stand alone two dimensional form or attached to any product.
So assuming that you're not planning on creating a company known to the public as "Have a Nice Day" -- or any of the phrases you've come up with -- you're best approach forward is to work with a copyright attorney to protect the designs you want to affix onto products. Good luck.
The above is general information ONLY and is not legal advice, does not form an attorney-client relationship, and should NOT be relied upon to take or refrain from taking any action. I am not your attorney. You should seek the advice of competent counsel before taking any action related to your inquiry.
The catch phrases applied to products are trademarks, as they would serve as indicators of a common source for the goods bearing those catch phrases. The designs are probably protectable both under trademark and copyright law.
Commonly used slogans such as "Have a Nice Day" are part of the public domain and it is unlikely you would be able to protect them for T-shirts without acquired distinctiveness due to secondary meaning (i.e. without use for long enough that they are no longer merely public domain slogans, but have through your efforts become more associated with you than with their ordinary meaning -- such as Coca Cola did with "The Real Thing" or Clairol with "Only Your Hairdresser Knows for Sure" or Avis with "We Try Harder", or Anheuser-Busch with an entire breed of horses - the Clydesdales".
You need to be aware that virtually every brand uses slogans and uses T-shirts so making common phrases into trademarks often takes huge advertising expenditures.
The artwork, however, if unique, will be more easily protected.
A good trademark prosecution attorney or marketing attorney will know how guide you in protecting the designs using copyright, trademark or service mark registrations, as appropriate, given your strategic needs.
So far, this is free to you. Until you pay a fee, I am not your lawyer and you are not my client, so you take any free advice at your sole risk.
Without knowing the exact phrases and designs involved, it is hard to advise you. Generally speaking, copyright law does not protect short phrases or names. However, depending on the circumstances short phrases or names may acquire the status as trademarks if your use of them in commerce is sufficient to result in their association with your company and its products in the minds of consumers. Designs on t-shirts that have independent artistic value can be protected by copyright, but you should know that copyright law protection for clothing designs is generally considered weak--most companies in the fashion business rely mostly on on trademark law to protect their designs against counterfeiting (this may soon change is Congress is considering legislation to strengthen copyright law as it applies to fashion).
Fundamentally, however, whenever someone embarks on an interesting project like this, it is really essential that intelletual counsel property is retained to advised on branding and design issues. I had a conversation earlier today with a client who developed a great new product---and invested his heart and soul in it---but failed to invest in an analysis of the intellectual property issues that might be involved in the situation. This client discovered today that he can't launch his product on the date planned because he failed to take into account intellectual property law issues when he began working on his product. This tragedy (and it is a financial tragedy for many clients) happens far too often, and would be avoided if persons in your position realized the need to work with (and pay) intellectual property counsel at a very early stage of developing your business plans.
Short phrases aren't copyrightable, so you can't prevent others from coming up with the same bumper-sticker-sized phrases. But those phrases might already be trademarked, so don't be so sure that they don't represent a company or a product if you haven't done a trademark search, which I doubt you have.
As for your designs, those can be copyrighted.
Each trademark costs $325 per mark per class, which means one for clothing, one for mugs, one for posters/calendars, etc. so you can see how that can add up fast. if you gtrademarked each phrase for 3 products that would cost $975 per phrase.
Each copyright costs only $35.
I think what you should do is trademark your COMPANY NAME, not any particular phrase, which is really more of a design element anyway, as the SOURCE of those t-shirts, mugs and calendars, using labels and hangtags to show that company source. That allows for maximum creativity at a more modest expenditure of IP rights. See an IP lawyer for help.
Avvo doesn't pay us for these responses, and I'm not your lawyer just because I answer this question or respond to any follow-up comments. If you want to hire me, please contact me. Otherwise, please don't expect a further response. We need an actual written agreement to form an attorney-client relationship. I'm only licensed in CA and you shouldn't rely on this answer, since each state has different laws, each situation is fact specific, and it's impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue.
This may not apply to your products, but is something to ask your IP attorney. Depending on the types of designs and your products, you might consider filing for a design patent. Generally, a design patent protects the ornamental design of a functional item, examples of which are the shape of a soda bottle, a search engine home page, or the look of a loud speaker.
As I said, this may be inapplicable to you, but is something to consider.
Best of luck!
Legal disclaimer: This answer is not legal advice, but is for informational purposes only. My answer to your question does not create an attorney-client relationship between us. Please contact a licensed attorney in your area for competent legal advice.