AUSTIN — Texas Republicans picked the state’s attorney general in the fight to succeed longtime Gov. Rick Perry, while a rising Democratic star from Fort Worth coasted to her party’s nomination Tuesday night during the nation’s first statewide primary.Warnings about Democrat Wendy Davis’ star-making run for Texas governor threatening two decades of Republican dominance dealt complacent conservatives a new reason to vote. So did a rare opportunity to select an entirely new stable of leaders after 14 years under Perry. “I want you to know this: I am ready to fight for you and every hardworking Texan across this state,” Davis told a packed house of pumped up supporters at her victory celebration in Fort Worth.The Republican primary victor, Greg Abbott, said he, too, is ready to move on to the campaign leading up to the November showdown with Davis. “It’s time we turned our eyes toward the general election,” Abbott said at his celebration in San Antonio.Perry’s decision to not seek re-election launched a stampede of 26 Republican candidates vying for six of Texas’ top offices. Among them was George P. Bush, the 37-year-old nephew of former President George W. Bush and son of former Florida Gov. Jeb Bush, who easily won the nomination for land commissioner in his political debut. In the first primary since Ted Cruz barreled into the U.S. Senate in 2012 and yanked Republicans nationwide further right, Texas candidates willingly went along. U.S. Sen John Cornyn, who didn’t get an endorsement from his fellow Texas senator, routed his primary challenger. “I say they are not going far right enough,” said Marlin Robinson, 56, after casting his primary ballot in Houston. “They need to go further right as far as I’m concerned because I’m tired of this liberal crap that’s running this country.” Abbott clinched the Republican nomination for governor and Davis locked up her party’s selection, thereby making official a showdown poised to become a record-shattering arm’s race of fundraising in a Texas gubernatorial election. Democrats set on breaking the nation’s longest losing streak in races for statewide office hoped a charismatic headliner in Davis would turn out long-dormant voters. Underdog raceDavis, who catapulted to national political stardom last summer with a nearly 13-hour filibuster over abortion restrictions, is the first female gubernatorial nominee in Texas since Ann Richards in 1994. “Now is the time to fight for our future,” Davis said at her Fort Worth rally. “This is not the time to stand still. As governor I will fight to give our kids a 21st century education.”Added Davis: “This campaign, this fight is for millions of Texans, who want our kids to have a 21st century education. Texans who want to create an economy and jobs for the future. Now is the time to give our kids that education.”Davis blasted Abbott as “just a defender of the status quo.”Her underdog campaign has raised $16 million so far behind a whopping 91,000 individual donors and big checks from abortion-rights groups. “If people don’t start supporting the Democratic Party and voting as a Democrat, instead of being a Democrat voting in the Republican primary, then we’re never going to win races and we’re never going to establish ourselves as a serious party here,” said Janet Veal, 43, a student adviser at Texas Tech University. That possibility, and the rising influence of Cruz, has Texas Republicans flanking farther right this primary season. Some pledged to further tighten some of the nation’s strictest abortion laws and double down on the state’s gay marriage ban – one of several state bans recently ruled unconstitutional by federal courts. “I think we need to bolster the border security and get tougher on immigration,” 38-year-old conservative Republican Glendon Paulk said after voting in Lubbock. “I’m all for people who come over here legally but the illegal immigrants, it doesn’t make sense for them to get a break while we’re working and having to pay taxes.” Frigid weather greeted some voters with a dangerous drive to the polls. Austin locations opened late because of icy conditions and extended voting for two hours. Turnout was light in many places, with election workers seen knitting or reading a newspaper in between voters’ sporadic arrivals. The last time Texas had so many open statewide seats was 2002, when Perry won his first full term. While Democrats are running mostly unopposed in their primaries, crowded fields in the Republican races for attorney general, comptroller and commissioners for agriculture and railroads make May runoffs likely. Limiting governmentAbbott is the GOP’s first new gubernatorial nominee other than Perry to appear on the ballot since George W. Bush in 1998. Speaking at his victory party in San Antonio, Abbott accused his opponents of trying to expand state government. He said, “I say no way to bigger government in the state of Texas.” Abbott pledged to fight for low taxes and to prioritize education. The 56-year-old Abbott has been attorney general since 2003 and is a former Texas Supreme Court justice. His ambitions to succeed Perry were no secret while spending years stockpiling more than $20 million in campaign cash for a gubernatorial run. A big emphasis for the GOP in the general election will be Hispanic outreach, Abbott said.The Texas attorney general said after voting Tuesday in Austin that Republicans “are going to reach out and be more inclusive” of different cultures than ever this election year. Hispanics are the fastest-growing population in Texas and their voting power is strengthening. Phone banksEarlier Tuesday, hours before the polls closed, Davis met with volunteers making phone calls at her phone bank, who were urging voters to get out and vote.She applauded the volunteers, saying “there was a day when I didn’t have nearly as many of you to help me.”After hugging a volunteer, she sat down to make some calls herself. Both calls she made ended up going to voice mail, and she left messages urging them to cast their vote Tuesday.Another volunteer who was talking to a voter handed Davis the phone. She smiled and nodded. “I promise I’ll make you proud,” she told the person on the other end of the phone.Texas Democratic Party Chairman Gilberto Hinojosa said Davis indeed already has made his party proud.“Her leadership has sparked a movement across the state that is firmly focused on the future. Wendy Davis is a proven fighter, and she is ready to lead for our schools, a better economy, and more jobs,” Hinojosa said in a prepared statement.Illinois holds the nation’s next primary March 18, followed by a flood of state primaries in May and June. Staff writers Anna M. Tinsley and Mitch Mitchell contributed to this report.