She brought both weapons in an attempt to portray two perpetrators. I don't think she ever thought they would question her - that they'd be looking for two perps.
Stabbing first: It's really personal. He was rejecting her, and she couldn't stand it. People like Jodi don't take getting dumped very well. She was going to stab him in the heart, like he figuratively did hers.
But then he struggled. He fought her and it made her even more mad because now he was really putting her out. She'd planned all the blood to end up in the shower and now he was making a huge mess and taking more time to kill.
Once she slit his throat and put an end to the struggle, she dragged him back in the bathroom, remembered her two assailant plan, and decided to shoot him in the face for messing up her plans and making such a bloody mess. It was the last FU Travis.