Personally, I have been very happy with my Fluke Model 26 III. If I recall correctly, it is a "ruggedized" version of the Model 77. The reasons I like it are: It is Auto-Ranging, as Grainger mentioned; it powers itself off after a certain amount of time of inactivity, which has saved me on batteries; besides the basic functions of a DMM, it also operates as a frequency counter, at least within the audio range, and it has a small range of capacitance checking.
You will not need these extra features to complete your Bottlehead kit, of course, but if you get the "bug" and decide to pursue this hobby, they are handy features to have!
As far as hand tools are concerned, you may already have what you will need: A selection of screwdrivers; small nut-drivers are handy, but not absolutely necessary; needle-nosed pliers; a good wire-stripper; a good soldering iron in the 35W-45W range, with small screwdriver or chisel type tip. It is nice to have a stand for the iron, and a cleaning sponge you can keep damp to wipe the iron as you use it.
There are other "nice-to-haves", but this should get you started.
