[R] Classification methods - which one?

[Peter Kupfer]

Dear all,
i searched for some classification methods and I have no glue if i took the right once.
My problem: I have a matrix with 17000 rows and 33 colums (genes and patients). The patients are grouped into 3 diseases.
No I want to classify the patients and for sure i want to know which rows are more helpful for the classification than others. 

I tried SVM and random forest. Do you think this are the right classification methods? Maybe there are some hints you can give me. I am more familiar with the Bioconductor packages. Furthermore: This is/was not my field of study in the past but I want to understand it and I am willing to deal with this field.
Would be amazing if one of the (more) mathematical people can give me a hint. 
Thanks and all the best

Peter


PS: I can upload my underlying data if somebody is interested