Hi Falco, For external threads you should use the nominal diameter i.e. 4; 6; 8 mm etc but I agree starting the die can be a little difficult.
You should always put a chamfer on the end of the bar to the depth of the thread and when starting in the lathe there are several things you can do. I usually start the thread by using the tailstock but lock it on the bed and apply a gentle pressure as you start the thread, you have to make the die "bite" into the work and it will not do this unless you apply some pressure to feed it in. It is a matter of "feel" when doing this.
Another approach is to put a taper on the work or reduce the diameter for a short length [as you have already found out] then remove this when finished.
On large threads it is helpful to truncate the thread diameter by a small ammount, as a guide use 1.5 percent of the diameter per 0.100" e.g. a half inch thread reduce by 0.0075" This is not definative but it works well, to be correct you would need to consult the relevant BS tables but for ME work it is OK. Not necessary when screwcutting them for metric threads but you do need to truncate imperial and unified threads unless you are useing a full form cutter. [sorry digressed a little there]
HSS vs CARBON, generally HSS will be a better quality and the best are ground thread dies & taps but they are considerably more expensive. Carbon will cover most of you needs but I usually byt HSS ground thread to H6 tolerance.
Hope this helps a little.
Regards John