This isn't so easy to answer, because the constraints are fairly specialized.
The following considerations can be made, though:
- BIGQuery is not yet public. Thus, with a small usage base, even if you are in the preview population, it will be harder to get advice on improvement.
- Each of your answers asked about a modeling system & a storage system. Apache Mahout is not a storage mechanism, so it won't necessarily work on its own. I used to believe that its machine learning implementations were a a pastiche of a few Google Summer of Code, but I've updated that view on the suggestion of a commenter. It still looks like it has rather uneven and spotty coverage of different algorithms, and it's not particularly clear how the components are supported or maintained. I encourage an evangelist for Mahout to address this.
As a result, this eliminates the 1st, 2nd, and 4th options.
What I don't quite get is the need for a real-time server to utilize Hadoop and RHIPE. That should be done in your batch processing for developing the recommendation models, not in real-time. I suppose you could use RHIPE as a simple one-stop front end for firing off queries.
I'd recommend using RApache instead of RHIPE, because you can get your packages and models pre-loaded. I see no advantage to using Hadoop in the front end, but it would be a very natural back end system for the model fitting.
(Update 1) Other interface options include RServe (http://www.rforge.net/Rserve/) and possibly RStudio in server mode. There are R/PHP interfaces (see comments below), but I suspect it would be better to access R through HTTP or TCP/IP.
(Update 2) Addressing the whole process, the basic idea I see is that you could query the data from PHP and pass to R or, if you wish to query from within R, look at the link in the comments (to the OmegaHat tools) or post a new question about R & SimpleDB - I'm sure someone else on SO would be able to give better insight on this particular connection. RApache would let you instantiate many R processes already prepared with packages loaded and data in RAM; thus you would only need to pass whatever data needs to be used for prediction. If your new data is a small vector then RApache should be fine, and it seems this is correct for the data being processed in real-time.