The train from 30th St. station to Drexel is the R8 Chestnut Hill West line (at the Queen Lane stop). 🙂
I'd definitely suggest arriving in Philly sometime the day before via the NJT/Septa trains (which will connect in Trenton). You might be able to stay with a student which would make it a pretty cheap trip overall. If not, there's any number of hotels recommended on the brochure. The one I stayed at last April was the City Line Holiday Inn on Presidential Boulevard - pretty close to the med school and they gave free transportation to and from Drexel on interview day!
For more info, do a search for a poster named kaos - he/she recently interviewed at Drexel and had similar questions. 🙂