What subway do you take from Penn station to get to spring st?

You could take the Downtown C train (of the A-C-E, the blue line) from 34th Street-Penn Station to Spring Street (at 6th Avenue). Unless you are traveling late at night, in which case you take the A. The C (a local train) doesn't run at night, so at night the A, an express train, runs local.

Then you'd walk 7 blocks east to Broadway. They're short blocks, so it's only about a third of a mile.

But if you really don't want to walk, then you can take the Downtown A-C-E from Penn Station to West 4th Street (doesn't matter which you take) and then transfer at West 4th to the Downtown B-D-F-M, the orange line, (again, it doesn't matter which train you take). Take the Downtown B-D-F-M to Broadway-Lafayette.

You'll exit the subway at Houston Street, between Broadway and Lafayette Streets (actually, Crosby Street runs between Broadway and Lafayette Street, but it's a minor street). Walk 2 blocks south on Broadway to Spring Street.