It depends on what kind of biostatistics you are about, as the particular questions of each field differ a lot and the basic handbooks are usually too much focused on exact cases. But generally, I recommend work of R. D. Peng, for free accesiable on Leanpub (e.i.: https://leanpub.com/artofdatascience). As biostatistics is mostly done in R software, I recommend you to make some R courses on Coursera, the best one I experienced, is guaranteed by John Hopkins University (https://www.coursera.org/specializations/jhu-data-science).
Thank you so much for the suggestions. It looks like the "Art of Data Science" handbook is not free of charge but I still appreciate the recommendation!
I agree w/ what Krystof said above, and would strongly recommend Roger Peng's book and course at Hopkins for the how to do (methodology) the analysis. Another book that I would recommend for beginners is this book:
This book is less about how to do it, but more speaks about why to do it. It's a book that shows the kind of problems that people who first came up with the statistical solutions were facing and how they overcame them. The example of Gosset who worked at the The Guinness Beer factory is famous when he came up with the t-test, and this book gives such examples w/ historical context of the statistical tests and methods.
Actually, you can download it for free. You must choose the option you want only the book, not supplementary lecture videos, and then you can set the "you pay" scale to $0.
If you are looking for quick and objective information on how to perform statistical testing, including testing of each statistical assumptions to check if your data fit the test chosen, I strongly recommend you Jullie Pallant's SPSS Survival Manual. She goes straight to the point but also suggest you to go deeper in a subject when needed. This one is more focused on how to perform, interpretate and report statistical tests and results with SPSS but is useful to start with the very basis.
Another SPSS based book is 'Discovering statistics using SPSS' from Andy Field (there's also a version based on R). It goes deeper on the maths theory behind biostatistics but it is very 'user friendly' and often amusing, because of its informal narrative. It tells you why and how to perform statistics and also how to report it.
If you're looking for advanced multivariate statistics, which we have to face sooner or later when dealing with basic and clinical research, I recommend you 'Using Multivariate Statistics' from Tabachnick and Fidell. They're cited by several authors I read, including Pallant and Field.
Both books are focused on health and social sciences research questions. They helped me a lot to understand which steps I was suppose to take to test my data and why.
These tutorials help me a lot on the comprehension and interpretation of 2 ways ANOVA using IBM - SPSS. It is not expensive the access to all the information. I think is a good way to start to manage SPSS software and study statistics clearly.