Park Tool offers a
home mechanics headset press, but you will see that it is little more than the threaded rod with plate washers mentioned in previous posts. I have one and it works well.
Chris King headsets are great but you will also need the special CK pressing kit and a crown race installer.
The Cane Creek 40 is a good choice for a home build since it has a split crown race so the headset press is the only tool required.
Having recently purchased a Cane Creek 40 I think I can anticipate your next question. Which one? It is offered in 40 standard configurations. Upper and lower assemblies are also sold separately to add to the likely confusion.
However I believe configuration used in the LHT is the
40.EC34.
The type of bottom bracket will be determined by your choice of chainset. Square taper cartridge type bb's are the most commonly used on touring bikes, but modern chainsets may use a hollow axle and external bearings. Both are easy to install but you will need the right tools for each one. It is worth consider the purchase of a home mechanics toolkit which would usually include standard bb tools and more.
Steerers are easily cut to size with a hacksaw using a pair of worm drive hose clamps as a cutting guide, but my tip would be to leave it uncut if possible. On a touring bike the rule of thumb is for handlebar height to be roughly the same as saddle height. You may need an angled stem to achieve this even with the steerer uncut.
I have acquired most of the components I need for my third bike build. It is satisfying and addictive.