First off, :welcome:
You can find lots of help with heat pressing and heat transfers in the
Heat Press Section of our forum here:
http://www.t-shirtforums.com/forumdisplay.php?f=15
Browsing through some of the recent discussions on that page should give you some great information on printers/inks/papers to use.
You can also use the forum search feature, and search for the keywords: paper or best or printer or inks to find past topics that could answer your question.
I think what you're looking for is pigment ink, which may or may not be available for your HP. Which HP model do you have?
Also, you won't get good results at all using a hand iron. From the threads I've read (and I'm no heat press expert), you'll need to get a professional heat press machine that will give you consistent pressure and temperature to get a quality looking heat transfer.
I think I read somewhere about a paper called "iron-all" that is supposed to work ok with an iron.
Maybe someone else with more experience will be able to help more.
Again, welcome to the forums!