Please give me some school recommendations

[catharole]

Hi everyone, I'm currently looking into graduate schools for bioinformatics and leaning towards masters because I feel like I'm not competitive enough for a top PhD Program yet and was wondering how competitive am I for masters/PhD. Would it be considered a better choice to complete another masters and gain more research-orientated experience before I apply for PhD Programs again? 

Undergrad Institution: New Zealand (81 overall in QS ranking)
Major(s): Biomedical Sciences
Overall GPA: ~3.7

Graduate Institution: Australia (45 overall in QS ranking)
Major(s): Software Engineering 
Overall GPA: ~3.8

Research Experience 

• Research assistant at a lab focused on stem cells, not much publications etc. made mainly just contributing to the project as a technician 
• Research project for half a year related to bioinformatics and using machine learning to map out genes related to kidney cancer (likely to be published by the end of the year) 

Universities for Masters 

• Standford  
• Cornell  
• UCLA
• Brown  
• Harvard  
• Penn State

University for PhD Programs 

• Harvard -  BIG Program  
• Duke -  CBB Program
• University of Pennsylvania - GCB Program
• Yale - CBB Program

I know some of these programs especially for my PhD choices are particularly competitive however I found that a lot of them seemed to particularly align with my interests in genetics and software and some labs have professors who I know are doing research in the area I have a particular interest in. I would also appreciate any recommendation for schools which may be more suited for me currently.

Edited September 5, 2020 by catharole

[BabyScientist]

I think a second masters would serve you less than a research position if you ultimately want a PhD. Your application is fine for a PhD, depending on your LORs and SOP, but not for programs of that caliber. A research associate position would give you opportunities for publication that will certainly help.