Safety: Among the safest neighborhoods in the city, though Portage Park can get slightly ragged along its southern border (Belmont corridor).
Rent: Portage Park will be cheaper than Jefferson Park, which in turn will be quite a bit cheaper than the "fanfare" neighborhoods on the North Side such as Lakeview, Lincoln Park, Bucktown/Wicker Park, etc. Expect a decent-quality 1-bedroom to start at about $750/mo in Portage Park, and about $800/mo in Jefferson Park. Add about $125 to each for starting rent on a 2-bedroom. To get an idea of what your money will get you, check out
Chicago Reader Spacefinder and use the filters to select the neighborhood, # of bedrooms, etc. Many ads will include pics.
Transportation To City: Jefferson Park is extremely convenient because it is the convergence point of a Metra train line (two stations), the CTA Blue Line (one station) and the Kennedy Expressway. This is why Jefferson Park is more expensive than Portage Park.
Portage Park is only convenient in the very northeast corner of it where there is access to the Jefferson Park Metra and CTA stations, the Metra Mayfair station and the Kennedy Expressway. The further west and south you go in Portage Park, the more you have to rely on unpredictable bus lines to connect you to train stations to get you downtown, or the more street-level traffic you have to endure to get to the expressway.
Stores/Rest/Things To Do: There are plenty of grocery stores and what-not in each area, so you'll never have to drive too far to do a grocery shop. There are also lots of mom-and-pop storefronts in each. As for things to do, well, these are not "nightlife" neighborhoods. They are bedroom neighborhoods with kids and families. Portage Park in particular has a major Polish contingent. And by "Polish" I don't mean "they are the 3rd-generation descendants of people who came here in the 20s and 30s." I mean "they just got off a plane from Warsaw last April." The bars in both areas are local hangouts (which in Portage Park means your English-speaking self may be considered something of an interloper unless you can converse in Polish) and the restaurants serve down-to-earth food. But the advantage to living in Jefferson Park is that you have access to lots of "hip" nightlife spots via the 24/7 Blue Line (direct access to Bucktown/Wicker Park) and the 24/7 Lawrence bus line (direct access to Lincoln Square, Uptown, Andersonville, indirect access to Lakeview/Wrigleyville and Lincoln Park via connecting 24/7 bus lines or the CTA Brown Line that runs pretty late into the night).