Probably something like this. They are a classic design, found new and used in many places and inexpensive. I have a half dozen or so of these little guys scattered around the shop so one is only an arms length away. They can be found in boot sales quite often for a few pounds/dollars.
http://www.record-planes.com/record-no- ... ock-plane/
The key is that the tool be sharp and set up properly. If you haven't any experience with that, probably your local luthier or school which teaches wood working or a good traditional cabinet/furniture maker could help you with that. New planes also need a bit of tuning and sharpening right out of the package so you don't gain much by buying new if good used ones can be found.
Hide glue is more traditional and used by many luthiers. As to if it is better than synthetics, that is arguable and luthiers often do argue over this. I use it and fish glue most of the time, partly because I build historical instruments and partly because it suits my work process better than other adhiseves. Hide glue is easy to use but may take some practice and planning if you've not used it before. You have a relatively short working time, compared with Titibond, before it starts to set/gel, so if one is just starting out building instruments and have little experience with using hot hide glue then I don't suggest it.
IMO Fish glue, a very ancient advesive, is a good alternative which is used by many luthiers for some if not all applications. There are supposedly a few drawbacks with fish glue which you will read about in various discussions, but I've used it for nearly 20 years for many applications and never had any issue what so ever. I've found most arguments against this glue largely unfounded...but that is just my experience.
Since this is your first instrument I'd probably go with the EMS recommendation. Just the Titebond Original, creamy coloured wood glue. The other versions II, III and IV sound good, and they are excellent for the applications they were designed for, but since they are actually more specialized use glues (for example, Titebond lll was designed at the request of wooden boat builders where a waterproof adhesive with a little flex is ideal), they are not appropriate for most musical instrument work.
Just my thoughts, others may have further suggestions...