Hi Ivrie,
Tim has pretty well settled the issue between iMAP an POP and as he said you do not want to mix the accounts. Here is what I would do. Don't know what kind of IMAP account you have (I have Yahoo) but Gmail and others should behave about the same.
I just went to my computer which was logged on to Yahoo Mail. Yours may/will be somewhat different if you are not using Yahoo but you will get the drift. I added a folder under my "Folders" drop down, created a new folder called Test, and then added an email from my Trash to Test. Then I went to my iPhone and did a hard reboot as follows: "Hold down the Home and Wake/Sleep buttons at the same time for about 15-20 seconds until the Apple logo appears. Ignore the "Slide to power off" text if it comes up. You will not lose anything."
After the reboot, as expected, I could see the new Test folder on my iPhone (you will need the reboot first) and Test contained the junk email I had added. I then deleted the junk message from Test on my iPhone. Then I went to my computer and looked under Test and the junk email I had just deleted on the phone was gone. All of this was as expected, no surprises there, just wanted to insure before I replied to you.
My suggestion is that you do the same, move your less desirable messages (not your trash) into the "Test" folder (named as you please). This, again as expected, will not affect your ability to Trash messages and thus all will be synced across without cluttering your Inbox.
That is my recommendation. I hope it works for you as well...
elcpu