A more challenging way to participate in party politics is to run for a party's nomination to a specific public office.
Usually, this would be for a state-level office since local and municipal elections in Texas are typically nonpartisan - the candidates do not run as nominees of their parties. But, if you're worried about starting out too big, remember that a local elected position that is technically non-partisan can serve as a solid springboard into party politics.
Many state-level offices are local or regional in nature. The state of Texas is divided into 150 districts for the Texas House of Representatives and 31 districts for the Texas Senate. So you don't have to run state-wide, but only in your district, which is much smaller. All things being equal, the smaller the district the easier it is to win the nomination. These offices draw relatively little attention from powerful special interests and the media, and even less attention from voters. Therefore, a small but determined campaign organization has a relatively good chance of success.
The two major parties can recommend professional campaign schools that train prospective candidates for public office in how to plan and execute a successful electoral campaign. Universities and interest groups also offer training and seminars on the mechanics and techniques of running for elected office. For example, the New Politics Forum at UT Austin's Annette Strauss Institute, provides non-partisan seminars in the fundamentals of campaigning.