My personal feeling on why she used the knife first to attack Travis...
The plunging of a knife through her lover's naked, wet skin and into his body was as personal a way to kill him as there is.
In a sense, she was finally 'penetrating' him. She would have eaten him alive if it had been possible, she was so consumed by her obsession with him. She may have even perceived a morbid sense of intimacy with him in this death struggle.
I think she sliced his throat to silence his screams. She plunged that knife in so deep, and ripped it across his neck with so much fierce strength, she almost took his head off.
Pulling him back down the hallway and into the bathroom, and then shooting him in the head was done simply out of panic, I think. She had no way of knowing if his prior screams had been heard, and if outsiders may soon be busting down the door. In her fantasies of killing him, she probably never anticipated the noise.
I don't think the blood and gore bothered her very much. I do believe her fear was of getting caught. Anyone looking to buy her a birthday present should just send her blown up pictures of Travis' autopsy photos to wallpaper her cell room walls. I bet she would never tire of viewing them.
I think that with his death, by her own hands, she finally felt she 'owned' Travis, forever. And, also in his death, she exacted her revenge for a love unreciprocated. Like a 21st Century Betty Broderick. "Hell hath no fury like a woman scorned", and all that. She knew she was losing him. She'd rather have him dead than not have have him at all.
I think she "brought the gun to a knife fight" because it was her insurance policy and her back up plan. If things got too out of control, she'd just shoot him. Like she did, in the end.
Who knows? Maybe the gun was her way of making sure he let her in his house.