Because study is motivated by your job, I suppose you are mainly interested in
procedures rather than theory at the start. Except for Kaplan-Meier, satisfactory introductions to all
of the tests you mentioned can be found in almost any calculus-prerequisite
statistics book. Everyone has their own favorites, and there is no reason for you take advice from any one of us over another. Kaplan-Meier is usually covered in courses on survival analysis.
The American Statistical Association manages a couple of major meetings each year, the Joint Statistics Meetings in late July or early August; and another about six months later devoted mainly to statistical practice (www.amstat.org). I hope you will be able to attend one of these meetings soon. Goals should to find out about new developments, to network with other statisticians with similar interests, and to visit the vast display of books from various publishers where you can browse what is available. Outside North America there are the International Biometric Society, the Bernoulli Society, and the (British) Royal Statistical Society, among many others. (All have web sites; many have reduced membership rates for people transitioning from university to
You should try to accumulate a reference library of general statistics books (z tests, t tests, Wilcoxon tests, etc.)
books on experimental design (ANOVA), and books on regression analysis. If as i suspect) you
are in a health-related industry, you should include books on biostatistics
and survival analysis.
For specific topics, you can also get good help on the Internet: from university course notes, software user groups, discussion boards of statistical societies, and often Wikipedia. But choose your sources wisely because there is a lot of incorrect and misleading 'information' on various web sites.
Whatever books you choose, I hope you will start to become familiar with
statistical software. As you learn each new statistical procedure, you can
see how it is implemented in software for practical use. Traditional
software packages are SAS, SPSS, and Minitab (all fairly costly for commercial use), and R and Python (excellent, free, open source software). SAS is widely used in biostatistics; Minitab is widely used in quality management.