ha ha I meant jump the starter. If your batt's fine, then you can take some jumper cables, and carefully attach one set to the batter. then take the ground to the chassis of the starter, one to the positive terminal. make sure you hold the starter to the concrete with your foot, because it will jump and most likley scare the **** out of you even though you expect it. if it doesn't engage, then you know it's a bad starter.
If you insist on taking the starter in, may as well take your batt in at the same time and get them to try both. If you decide to test the starter in your garage, then after testing it and it checks out, I would take off the battery terminal clamps and charge the batt. You might have something drawing current that stops the batt from charging. If in the morning the battery dies prematuraly, then it's a bad batt. If it dies very slowly througout the day, hook the multimeter to the battery terminals, make sure everything in the car is off, get a person in the driver's seat with the door closed to take out fuses one by one (and put back after one by one) while you stand with a dmm on the battery terminals. As soon as you see the voltage stop dropping then you know whatever fuse was just pulled is still pulling current.