Hello and welcome to Morrowind and the modding community! Next time, you should post in the Mod forum, as we will be able to better help you there.
I am pretty sure Tamriel Rebuilt is compatible with both Rebirth and the Overhaul. However, as I don't use either, I am unsure if the Overhaul and Rebirth are compatible as well. You might want to ask in the http://www.gamesas.com/topic/1348329-rel-morrowind-rebirth-16/. I don't know a thing about Gratuitous Violence either, so you should ask in http://www.gamesas.com/topic/1179276-relzbeta-gratuitous-violence/.
Other mods? This would depend on your tastes and what you want to see in your game. There are many different mods out there. Below are some links that are very popular suggested lists.
http://www.gamesas.com/topic/1305729-mod-recommendations-for-new-players/
http://btb2.free.fr/morrowind.html
http://arcimaestroantares.webs.com/suggestedmods.htm
http://www.somethingfornobody.com/2011/morrowind-modding-guide/
You can also find mods at http://tes.nexusmods.com/, http://planetelderscrolls.ign.com/, http://www.elricm.com/nuke/html/modules.php?op=modload&name=Downloads&file=index, http://mw.modhistory.com/, and http://www.fliggerty.com/phpBB3/.
For correct mod orders for pretty much every known mod out there, you should download and run http://code.google.com/p/mlox/wiki/Mlox.