When applying for my PhD in the UK with funding I needed two letters of reference.
The first one was my Master's Dissertation supervisor, I would really recommend trying to get a professor that has worked with you before in a research sense (if possible), if this is not possible I would try to open up the conversation with a great research proposal. If the Professor is interested in it and you do a good job then he would be able to see that you already have some good research skills, a good proposal is the start of the project.
The fact the you have co-authored with the Ph.D student is good, they can mention it in the LOR.
The second letter of recommendation I got was from a Senior Lecturer in Finance, I could have tried to go for another professor but I did think a more personal one from even a junior member of the faculty would be better (similar to a PhD writing for you).
I would recommend trying to work on the professors that you already have, if they send two great letters, the third one becomes much less important.
I am also extremely introverted, however, you have to try, you have to stop by there office hours, (it gets less daunting each time), you have to go back even when they are to busy on a certain day. Win them over with a good proposal, if at all possible try to cite them in your proposal. Do whatever it takes, getting a PhD place is not easy, there is lots of competition, other people will be persevering with the small talk. Its like you're in a race with them, run faster.
Also the fact that you have publications is already a big thumbs up. You have a proven research record, that is far more than the majority of PhD applicants.
It is also good for the PhD student to frame the letter well if they frame it as your co-author rather than pal that could be better.
A last note on your Instructor without a PhD. There are some people in Universities that don't have PhD's but are still world-class researchers. I have met a few that have come from industry and rightly or wrongly, they would never bother with the fees for a PhD and their publications speak a lot more than the title, so double check if your instructor has good publication. Also, teaching experience is extremely important...
So if it was me I would probably go with the instructor that you have been a TA for and the two Professors. The fact you have written papers will come up in your application anyway, the University can judge how well these are with reading them, looking at what journals they are published in them etc. It is much more difficult for them to judge if you are a good teacher or not, so signalling this to them by a LOR from an instructor would be my best bet.
In my PhD interview, I was asked a lot about teaching, its important for the modern academic. As there is so much competition, they want good researchers and good teachers, not just one or the other.
Best of luck!