Texas allows you to complete a driver safety school.
You can do it online.
If you complete the school, the citation is dismissed and will not appear on your record.
Here is one school, there are many you can complete in person or online:
http://www.idrivesafely.com/
You can also ask the court to place you on deferred adjudication and complete a 90 day probation. You do not have to report to a probation officer, just avoid NOT getting a ticket during that time. If you do, the ticket is also dismissed and disappears.
You can plead nolo contendre, and still get either sentence.
Bottom line, the ticket goes away.
People rarely beat tickets in Texas courts under the conditions you recite.
Texas uses JP Courts and Municipal Courts for these offenses.
Their function is to collect MONEY, your MONEY.
That is one reason Texas has no income tax.
If you lose, the ticket will remain on your record.
Your insurance rates go up, and you pay again!