In Maryland we have an option of Video toll. This is used by various rental agencies. I looked up Enterprise Rent a car as an example and copied this from their policy page:
The charge for TollPasstm Service under options 1 and 2 above is $3.95 per usage day, not to exceed $19.75 per rental period, plus the amount of each toll. There is no TollPasstm Service charge on rental days that you don’t use a toll road. The TollPasstm Service charge and the amount of each toll will be charged to the debit or credit card on file with your Rental Agreement and will appear separately from Rental Agreement charges on your credit or debit card statement. (See Additional Terms and Conditions below).
So, video toll on the Bay Bridge (4 and 1/2 miles long and scares me to death) is $6. eastbound and they only collect one way, so you would pay 3.95 plus $6 for the bridge crossing. Enterprise has options for installed transponders as well.
If you leave from College Park, UMD, the logical path would be to get on route 50 east and head for the bridge. No other tolls on this route. Not sure what other routes you may take that might also have tolls - I-95 between Philly and College Park has a number of tolls but some are northbound only and I haven't been 'into' Philly in quite a while.
This assumes a rental in Maryland, but since you are landing in Philly, you may want to check the options with whatever rental agency you would use there.
Anyway, what I would do is decide what rental agency you are going to use and check the rental for the toll policy.