Hi Julia. I'm a resident of deep SE Portland, or simply East Portland, and I very much like it. I moved this direction a year ago after simply being priced-out of NE. For example, the home you listed would probably be $500K+ in a "better" neighborhood, but out here you can still get 1.5 acres and a decent house without promising your firstborn, so more and more folks I know have been finding themselves moving this way. Yes, there's still some petty crime, but nothing scary, at least not in my neighborhood, which is getting better all the time. If you want to check out the crime and housing data for your possible neighborhood, check out http://www.portlandmaps.com/
, it's city run and has lots of great info.
As to Zeneger farm, those people are fantastic! They run the Lents International Farmers market, which is small but the only market in PDX not part of the "Portland Farmers Market" umbrella, so the vibe is wonderful and very friendly. For example, one fo the main honey-sellers often brings his hive with him to the market! Very cool. Also, Powell Butte is wonderful, but currently undergoing a major construction/renovation as the city is installing a water reservoir up there, so until that's completed it's not much fun to hike there.
Hope that information helps, let me know of you have any other 'hood specific questions, and best of luck with the moving plans!