Of course http://sfbay.craigslist.org/sby/ is the place to search. Your expectations of price are square with the market. The trailing link is to current rentals on craigslist <$1400. That's a dynamic link so the content changes.
If you're willing to commute it might be best to grab a clean, safe place downtown or very close and then take the time to learn the more distant options - there are a LOT.
If your'e looking for luxury apartments you may want to check out the 101 San Fernando complex
101 E. San Fernando St. Ste. 100 San Jose, CA 95112
I find Yelp to be helpful.
In walking distance to Cal Train Downtown Campbell boast more restaurants, bars and shops. The Campbell Community Center is nearby!
Los Gatos Rents are a bit higher, however there are several apartment complexes and light rail is still available.
I can be found enjoying any number of these locations on weekends if you want to meet up sometime.
A Pre-Welcome to San Jose! There is a link on my website for crime reports on the left too..links section