For your shifters any shimano road derailleur made for 7-10 speed should work okay (except 4700 series Tiagra). Shimano MTB derailleurs up to 9 speeds should also index with your shifters. You're right to get a medium or long cage for an 11-32 cassette.

Here's a good blog about Drivetrain Compatibility but my takeaway is that certain derailleurs are expecting the shifters to pull a certain amount of cable... so with the older shimano stuff all their derailleurs moved 1.7mm for every 1mm of cable pulled so that's why there is such a large amount of compatibility with the old shimano stuff but that system ran into limitations with 10 and 11 speeds so it's all been changed now.