Do you mean for analyses or for downloads and data-mining?
ArcGIS is the best for visualising the homeranges or for translating different formats into one database. For analysing: Ranges9 (by ANATRACK) or a tool for R by Johannes Signer jsigner[nospam]gwdg.de
Data-download depends on the manufacturer, they may have own software or you use e.g. movebank.
You should try out ZoaTrack.org. It's an online database and toolbox for analysing animal tracking data (applying location filters, removing erroneous points, extracting distance moved, home ranges etc) and there are heaps of real tracking datasets that you can play around with. It's also free.
I agree with most of what have been said. As much as I find spatial analysis in R convenient, it is challenging and tricky as a newcomer to get started with R on spatial data. I think that you should know what (and how) you would want to do process your data manually, e.g. in any GIS software, and then you should start thinking about doing batch data processing in R. As such, you will be able to understand what R is doing (in the best case), why the output is not as expected, and you should anyway check the data prior and after the processing in a GIS (or similar such as ZoaTrack) tool.
Unfortunately, often enough I found bugs in the algorithms, even in established software like ArcGIS and R packages, that I prefer to check results very thoroughly based on a randomized sampling principle. Of course, the amount of data coming from GPS collars is often so vast, that you'll not be able to check all of it, however it's better to run tests with a selection of data and check the results instead of "blindly" trusting the processing software. Believe me, you'll sometimes be surprised by the flaws of certain established processes.
As movement ecologists, we find it a pity that most of the data collected through (still quite expensive) GPS collared animals is still simply "analysed" by calculating home ranges and drawing some lines on a map. Movements of animals and the degree of quality and quantity of data collected bears so much more potential for research and ecological insight in animal behavior and ecosystem processes...
I hope that you'll enjoy your work with animal movement data. It's an amazing topic!
checking for mistakes (like0-0 data in the Atlantics) is quite important. This is why I prefere working with Ranges9 (8), and then go to more ambitious analyses in R!
And due to huge datasets I prefere using ArcGIS, as Q GIS is limited in its abilities!
By the way: Which species will you start to study?
Pascal's experience with bugs is shared, unfortunately. With reference to the comment on GPS-data being used simply for home ranges and lines, we can make you hopefully happy with our Walk or Stride chapter (attached).
In this context I avoid the "home" in animal range/distributions (bear, elephant, gorilla) by lack of a definition that would include all the empirical distribution patterns, be it seasonal, inter-annual or expansion/contraction trends therein as well as the scale issue involved.
Article Walk or stride? A question for roaming herds of elephants in...