Here's the build I use for most of times, (It has also awarness, and 2 lol traits as bloody mess and good natured)
Instead of pyromanics I would use brd's, but this is just my own opinion after playing long time with those broken perks.
It can craft armors, small guns and big guns, level 2 profession of each kind, got eaten bunch of lol-bps such as lsw, rocket launcher, metal armor mk2 etc.
It can do most of things alone, unless doing PVP, then it is shitty, and then - alt madness starts if you want to do MORE in game.
Another character I would just do would be SG + EW / BG + EW hybrid for farming guns and armors, and the last would be Slaver or Thief, then you can start doing PVP alts, because anymore are just obsolete, I would never go for finding BP's beacause this is job for no-lifes and I do not wanna spend it searching for stimpak bps.
The idea of having starting character is great, but now just obsolete, Better make 3 specialised character's as Krupniok says, than one "woodsman" alt, sorry, but 2238 showed it's logic there and if you want to be more economic you NEED to do it.
That's sad but true one, I won't argue what is fun for others, but for me it ISN'T making hoards of alts.(but meh, that's just my opinion).
(You can also do the "snake eater perk quest" at level 9 if you have first pyroamnic or brd, that makes you kill those nasty scorpions in one hit, because I failed to do that quest lolo).