When choosing a term to rank for, in my experience, choosing a term that has low competition means finding sites that rank top 10 that do not have high domain/page authority scores, relatively low moztrust/rank, and of course really low backlinks. If a site has 10 backlinks, as long as they're from sites that are under 50 DA, they're easy to rank for.
The reason you get different results from KW Difficulty Tool using quotation marks is because that tool pulls the top 10 google results for whatever term you put in. Generally, the top results are different when using quotations. I recommend you NOT use quotation marks when using the KW difficult tool.
I would do your own research and optimization and stay away from using someone elses work/data, to me, it seems prone for errors and miscalculations which lead to loss of money, time, and other potential fallout.