1) I did my UG thesis on statistics anxiety. At the time, I didn't know enough to do actual statistics research, but I was prepared to do research on statistics education. You mention you are willing to teach yourself R. You could do a small simulation study on some subject you find interesting, e.g., simulate data which violate to varying degrees the assumptions of a model you learn in psychometrics or multivariate stats and see how bad the estimates and standard errors get. Even if your research is not very original, the act of doing this will (a) force you to really understand the model you are working enough to simulate data from it and ( develop programming and simulation skills that most students in quantitative psychology PhD programs that I know didn't learn until part way through grad school. You mention a lack of guidance at your institution. I strongly recommend contacting professors you are interested in working with now and ask whether you could get some supervision/advice from one or more of their advanced PhD students or a post doc.Most would be willing to help, and working over a distance is something worth learning (my PhD adviser was only in town 3 months of the year and I did the rest of my dissertation advising over Skype). I would try people at WUSTL, UNC-Chapel Hill, Missouri-Columbia, UIUC, UVA, ASU, OSU, KU, Georgia Tech, UW Madison (Ed Psyc), USU (Psyc/Epidemiology). If you post what types of research you are eventually interested in doing, I could make more concrete recommendations.
2) R is invaluable. SAS is useful. Use SPSS only when you have to.
3) No, a major in psychology is not necessary. You would be better prepared with a major in math, statistics (if a UG major in stats is offered), or computer science while taking a handful of psyc classes (developmental, clinical, abnormal, social, behavioral are a good core and what ever else you think you would like to do research in). Although most students I knew in quant psyc PhD programs had a psychology degree, those with math or CS degrees were at no disadvantage in the realm of psychology and had an advantage in the stats classes and the programming skills needed to complete a PhD in quant psyc.In terms of course work, the most useful classes taken as an undergraduate were (in this order) programming, linear algebra, and multivariate calculus, followed by several ties among the advanced stats classes I took (but I can't tell you one that was most useful).