Yeah, I also prefer to check ranking in serps manually. Don't really trust those automated tools out there. As far as I'm concerned, they are quite inaccurate. They rarely show the same results when checking the ranking manually.
Regarding the time needed to rank for a phrase, I have to agree with Steve-Hostirian. It depends on the niche and how targeted it is. In case it is a highly targeted phrase, you might need some time and work to invest.