> Should I learn R or Python (nltk, scikit-learn, pandas etc.)?
Honestly, whatever is most convenient at first. Getting a good grip on your first one is orders of magnitude more important than what language or system it is, and since convenience and ease of use help a lot with focusing one's attention on learning an mastery, that's what counts. Eventually you might grow out of the one you picked, and if you keep coding stuff you'll inevitably branch out to other languages and systems. All the data scientists I know know and use both R and Python (with bells and whistles). All of them.
> Should I learn hadoop or focus more on machine learning techniques?
From what I read, and from what one of those data people told me, hadoop can be a waste of time in many situations. Namely, for almost anything small enough to store and process on a desktop computer, you'll probably do it faster using something else (and with less headache). But hop to page 8 of this survey for a better picture from the horse's mouth: http://www.paradigm4.com/wp-content/uploads/2014/06/P4-data-...
The rest of the survey I linked above is probably well worth your time as well. Obviously, take into account the survey was run and presented by paradigm4, and do your mental corrections and debiasing accordingly.
For smaller data sets, R will work, and Python acts as glue. In general, on a daily basis, I spend about 70% of my day finding and cleaning data (a lot of data scientists will say the same) and getting it in the shape I need, and only then running algorithms over it.
I work with fairly small-to-medium sized data (now..previously I was at Hadoop scale) and my tools of choice are: SQL for getting the data I need (you will need to become really good at SQL..almost everyone uses it everywhere, really great universal skill to have), Python (pandas) for cleaning the data and making that cleaning process reproducible, then high-level algorithm analysis in R, and presentation either in R or Tableau.
I would say learn A statistical computing language and a programming language. If you could mix the two (via apis or other) it becomes even better. I interface matlab+c and Ruby+R, the former for speed and performance, the latter to prototype.
Learn something statistical, be it R/Octave/Stata/Matlab. If you have a budget, go with matlab as there are lots of packages and scripts available, although R is catching up quick. If performance is an issue, R has caveats, since the vanilla version has no multithread support.
I don't know python and use C for everything, but there are so many packages for python, including (GPU accelerated) machine learning that it is IMO definitely the way to go in your case.
I would also get very comfortable with SQL - much of the data that you will work with in an enterprise setting will be accessible through SQL querying or some close variant.
If you come from a programming background Python will be more sensible and accessible for you as you learn. If you come from a more classical research background then R will generally be a more comfortable place to start.
Enjoy the journey
My vote is on Python. It's more broadly useful and R has some restrictions handling really big data sets.
>Should I learn Hadoop or focus on machine learning
Focus on machine learning. If you don't need to know the Hadoop architecture then don't learn it. If you're picking up machine learning and later find you need to know Hadoop, you'll be able to pick it up.
If you need distributed computing power for projects you are working on here are some options:
http://zillabyte.com/ http://databricks.com/ http://aws.amazon.com/elasticmapreduce/