R is certainly more useful than SPSS for performing certain analyses and I have found it super handy in the graphics department. It has some great options for visualizing outliers and via leverage and the like. I started with SPSS and switched to R, after only spending about 6 weeks with it, I started really realizing the limitations of SPSS. I'm a huge fan of R. I love how much control I have over my analyses and how it allows me to really dig my teeth into a problem.
Also, I expect having a grasp on programming is going to be invaluable to my career...
Now the answer to what you should do... it kind of depends on HOW you are using stats. I think of you want to be a stats expert, the go-to person, you will need R. Learn it as soon as possible start reading R blogs etc.
If however stats are going to be something you're going to use somewhat tangentially to your prime work then you could likely get by only on SPSS and consult with someone if you run into problems. Many many researchers have great careers doing just this... of course this is all just my opinion.
It partly depends on the area of science you are working. In certain sciences R is becoming a standard of fact. Many new methods are released in R. However, the main advantages is that R is a a programming language, therefore you can automatize your own analysis. In addition, it is free. I would recommend R over SPSS to any new scientist.
Just to add, R is far from obsolete. Actually by many accounts of growth and popularity, R use is growing while SPSS use is falling... At this point it seems safe to say that R is likely in an upswing and is quite incredibly far from being obsolete.
I used to teach both SPSS and R to psychologists. Most liked SPSS more, some liked R more. Because of the large number of packages R can do more, but if you like GUIs (graphic user interfaces), SPSS is good. I'll attach an R intro Kamala London and I did a few years ago, but there are lots of R sources out there.
ps. I spend hours everyday doing stats, and R is the main package I use. If you plan to spend hours everyday doing statistics then you will use several packages and R is good for that because it interacts well with other packages (from Python to BUGS to writing papers using LaTeX).
Chapter A very brief introduction to R (ch. 1 of Wright & London, 2009)
R program is most useful from SPSS for statistical computation, in the R program calculations is done at high speed and advanced computing is possible.