That's not as simple a question as it sounds. If you can provide the following information, I'd be able to tell you a lot more, though:
1) What was the specific offense?
2) What was the disposition? (dismissed, convicted (includes "just paying a fine"), or dismissed after deferred disposition).
3) How old were you at the time of the offense?
You ask if you can get Class C midemeanors expunged. The question might seem simple, but the answer is fairly complicated Class C misdemeanors include traffic tickets and any crime which is punishable by fine only. These cases are normally filed in municipal or JP courts.
For any Class C acquittal or outright dismissal (i.e.-you were never fined or put on probation), you could expunge the offense under Texas Code of Criminal Procedure (TCCP) Section 55.01. You should also be able to expunge any successfully completed Class C deferred adjudication under TCCP Art. 45.051(e). You can also expunge one "under age" alcohol conviction under the Texas Alcohol Beverage Code Sections 106.01 - 106.15.
The filing fees could be as low as $30 and as high as $282 or so, depending on the applicable code section, and other factors. I would suspect that you could find a local attorney to do the work for less than $1,200.
Because of all of the various factors, you should probably be speaking to lawyers (either in person or over the phone) rather than trying to get answers in a written forum such as this.
Best of luck to you!
This answer is for general purposes only, and is no subsitute for specific legal advice that would come from an attorney hired by you, having full knowledge regarding the facts and circumstances of your individual situation. This correspondence does not create an attorney-client relationship, and you should consult with one or more attorneys prior to acting on any of the information provided in this response.