Hey Sarah!
Welcome to the board and to Pittsburgh! 
Sounds like you got some great advice in here already, but I will add some extra nuggets!
a)If you are worried about $$, all you need to start & to keep you rolling is the patch kit, tire pump, tire levelers, and the tool-kit. For that, I recommend ((for affordability)), to just get the TOPEAK TOOL KIT. Found at REI, and for only $29.95, it gets you all above, and the pump comes with a bracket that you can attach to your bike & carry there.
http://www.rei.com/product/695177/topeak-deluxe-kit
NOTE: Granted there are other better bike-pumps out there, but this kit & pump has kept me rolling no-problemo, and for the price, pretty nifty too!
2) On the side, get an extra inner tube that you can use if on-the-rush to repair a tire. That way you just replace the inner tube, and then patch the old inner-tube at later on.
3) Get some cleaning & lubrican oil to keep your chain & drive train clean & running smoothly. Get some "Simple Green" all purpose green from any store ((like this: http://www.drugstore.com/popups/largerphoto/default.asp?pid=205364&catid=184274&size=300&trx=29888&trxp1=205364&trxp2=1)). And some "Epic Ride" as a nice lubricant: http://www.rei.com/product/712428/white-lightning-epic-ride-lube-4-oz
Just use an old towel or t-shirt to apply & wipe-off the material (follow instructions).
Personally, I'm not the greatest at keeping my chain clean, but do try my best! Once a week of lubricating will keep the chain happy 
4) Get some fingerless riding-gloves ((brand doesn't matter as much, just make sure that the gloves fit your hands and are snug on them)). The padding in them will save you stiffness/numbness in your hands. Plus, they usually have reflectance strips, which are helpful when signaling a turn on the street. Plus, in case that you ever fall in your bike ((hopefully never!!)), if/when you fall, the gloves will protect your hands from road-rash & tearing them apart. Plus, if you are all sweaty, the fabric in the gloves is good at wiping some of the sweat off your forehead 
5) A cage for a water-bottle ((more handy when riding than having it on your bag/pannier)) for hydration.
6) Helmet, locks & lights ((and sure you know all about that already)).
7) Always keep your eyes open on the road & pay attention -always!! Cars can change their mind, turn, run lights without warning!
REI recently had a free womens-mechanic class, where it showed how to change a tire & do basic bike maintenance. They might have more coming up soon. Although, as other have said, the interwebz, free ride, and asking people is just as good.
Personally, I patched my first inner tube & changed my first tire while following a the instructions online from a biking blog I google up! 
9)Don't know if anyone has mentioned to always also have some snack/candy/gigs newton/chocolate bar/banana/gu/cliff bar on-you as a "pick-me-up" snack food on the road. This is in-case you are tired or are low on energy, and you need some reserve energy to get home in decent shape. Personally, as a girl, I always have mini-chocolate bars, candy, or gu with me. Sometimes I do too much riding around, and when it comes time to go home, sometimes I'm feeling too whiped out. In cases like that I just consume one of the above, and it fuels me enough to get home.
Sure, you can always instead throw your bike in a bus rack and go home, but if you just want to GO, or are mid-way home and understimated your stamina to get there, the extra-energy snack will help you get there.
10)And.... have fun I guess! The rest of of it will come to you as you get more experience riding your bike & riding in the city -TRUST ME 
Okok.... hope this was helpful!!