hey freebird.
welcome to the board

ok, for recommended hotels/hostels in sevilla, scopee out the links below. Jeff's (the webmaster) site on sevilla is the "bomb"

so have a good looong look at the site for sevilla info. cheap? depends on what you consider to be cheap, it is all relative.
- sevilla hotels -->
http://www.exploreseville.com/hotel.htm#hotels- sevilla hostels -->
http://www.exploreseville.com/hotel.htm#hostelsalgeciras is where you will get the ferry to tangier. algeciras is 190km (118 miles) from sevilla.
looks like "linesur" (
http://www.linesur.com) bus company does the route in 2.5 hours. busses leave for algeciras pretty regularly from 6am to 8:30pm but the only daily busses are at 07:15, 10:30, 16:30, 18:30 and 20:30.
see
http://www.linesur.com/linesur/Horarios.html for the detailed timetables.
you cannot get a direct train from sevilla to algeciras which is why i have recommended the bus.
let us know if you have any more questions
saludos,
jer...