you'd spend less energy building a recycling plant on the moon, maintaining it, and flying junk to it than the energy required to actually hit the sun.
Your delta-V to hit the sun is roughly 30,000 m/s - orbital velocity.
Besides once you throw it in the sun it's gone. If you recycle it then you can move towards a low G shipyard on the moon...
Or if you don't like the moon, create a sub-geosynchronous (slower than geosynchronous) junk yard to slowly float junk to. Either way you'll have all sorts of orbits to collect junk in and massive plane changes will use most of your fuel.
---------- Post added at 12:55 PM ---------- Previous post was at 12:42 PM ----------
It would be interesting to try to hit the sun... If you were off just a little bit and missed the sun, then you'd create a nice man made object for the earth to one day hit a few years later.
Either way. I'd want a small guidance package on the the trash to keep it from getting into an orbit that may hit the earth.