Between a siddur (prayer book) and Tehilim (or other book of Nach), which should go on top? also, is there a distinction between printed or handwritten?
For reasons that I never understood, R' Aharon Feldman (Rosh Yeshiva of Ner Israel in Baltimore) said that "our" siddurim (which have Tehillim in them, and also a good chunk of Chumash, as well as other parts of Nevi'im in the form of select Haftaras) goes on top of a Tehillim and possibly even on top of a Chumash.
According to the Shulchan Aruch (Y.D. 282:19), the order for stacking seforim is a Sefer Torah on a Chumash; Chumash on Nach.
It seems logical that other books would go beneath these. I have heard (but never seen a source) that the writings of Chazal go after Nach, and then other seforim after that.
The Tehillim, being Nach, would presumably go on top of a siddur. The Shevet HaKehosi (2:299) writes that even siddurim which have the Tehillim in the back is treated like a siddur since that is its primary use and not like a Tehillim. (Interestingly enough, he also writes that a Mikraos Gedolos Chumash is treated like a normal sefer, since its main use is to learn the various meforshim inside.)
The Aruch HaShulchan (Y.D. 283:6) states that all printed seforim are equal in holiness when it comes to stacking them. So in this view (at least the way I understand it) it doesn't matter how you stack them, as long as any handwritten seforim (such as Sefer Torah, Megillah, etc.) is on top.
I couldn't really find a crystal clear answer on this topic, because it seems to be up to much debate and I couldn't find much help in online sources. (Because people are horrible at citing sources, you know?) With G-d's help this is something and perhaps it will aid someone else who knows more about this subject than I.