What resistance should I expect when testing capacitors?
I'm guessing that you are measuring these capacitors WHILE they are still soldered to the PCB?  If so, the resistance readings that you are getting are caused by the other components in the circuit.
Capacitors fail in a variety of ways.  One of the more common problems is that the ESR of the capacitor increases to the point where the circuit will not operate.  The cool thing about testing capacitor ESR is that it usually can be done while the capacitor is still soldered to the board.
Although there are several capacitor testers available commercially, it's fairly easy to build (or even bread-board) a simple tester that finds capacitors that have either failed OPEN or have had the ESR rise to unacceptable limits.
One such device is shown here: DIY Capacitor ESR Tester
You haven't said what kind of test equipment that you have available.  Hopefully, this helps a little bit.