With a 32t large cog on your cassette, you'll want a MTB or "mountain" derailleur. Road derailleurs seldom allow you to use a cog this large.

Shimano MTB derailleurs commonly come with two different cage lengths, noted as "GS" or "SGS." Since you're using a single chainring, you can use either cage length. If you had to run a longer chain to accommodate a triple crankset with your wide range cassette, you wouldn't have the option of using the shorter ("GS") derailleur.

If you use friction shifting for the rear gears, you have a slightly wider range of derailleur choice, since the derailleur is simply moving the chain from cog to cog and doesn't need to be compatible with a particular mfr's indexed shifting. If you use indexed shifting, you'll want to stick with a Shimano derailleur to maintain the same cable pull ratio. However, some of the newest Shimano MTB derailleurs pull a different amount of cable and won't be compatible for indexed shifting with your shifter.

Here is a nice Shimano derailleur that won't break the bank and is compatible with your needs.