tl;dr: Check out Finale Notepad
I'm a composer of classical music, and it sounds like you're looking at more pop-ish things, so take my advice with that caveat.
The big split in composing software is between Sibelius (which I think is better software by far) and Finale (which has a free version), so that's what I'd recommend to you. Both are expensive, but if you're serious about composing/arranging I'd recommend saving up for a full version of one of them (both have student discounts).
There's also a very powerful open-source notation program, LilyPond, but I don't recommend it if you're mostly interested in hearing chords: it uses a text-based interface (i.e. no GUI) with a steep learning curve, and it just generates a MIDI file, so the quality of the playback depends on your system.
Finally, for completeness' sake, Steinberg has an as-yet-unnamed program in development by the former Sibelius team (they were dumped when the program was acquired by Avid). For my money I'm betting that, when it's released, it will blow the current generation of composing software out of the water.