Assuming we talk sword user, i'd say Mechanics right after getting through main story in Junkyard (Depot A done), so about lvl 12sh: few more levels you'd be good using weapons sold by various merchants you get access to after Depot A (Core City, etc), plus possibly Claymore if you go get it, but quality 50 machete already does 1 point higher minimum damage than Claymore, so it'd make sense to me to max Mechanics starting at say level 12 and getting it maxed for current level by level 16 - at which time much higher than quality 50 machetes can be crafted and used.
Same for Electronics for power cores and modules when crafting them machetes. By level 16 you'd need 2x90 = 180 points spent into these two crafting skills, and with 40 points per level you get 200 skill points for levels 12, 13, 14, 15, 16 - meaning you still keep your Melee maxed during these levels and it's exactly 200. And to craft high quality ones, you'll definitely need 90 hard skill points in these two crafting skills, considering Int 4 hence no bonus effective points to these skills whatsoever. It's 80% of quality needed as effective skill value, so if planning for eventually crafting from quality 160 parts, then 128 effective skill is needed. 90 hard points + Hypercebrix = 105, +3 from food = 108, +15% on top from Your House bench = 124, so almost there. I'd say 93 hard skill points Mechanics and then only increase if really sure about it. As for Electronics, could possibly go with less than 90 due to available late-game gear with Electronic bonuses, yet on the other hand high quality shield emitters require lots more Electronics to make than Machete modules, so i'd still go 90 in Electronics (hard points) too.
Tailoring - i doubt Melee build needs any, at all. Good Ninja Tabi boots can be both found and bought (Constantine regularly sells 2k+ durability ones, that means they are 130+ quality), and spending whole ton of skill points to make a bit better ones does not seem a wise investment. Same for balaclavas. But if going for Tailoring to have all the utility of infused / expedition leather armors, then it's definitely a late-game skill to develop - i'd say possibly very last skill to start investing in, so some 20+ level. Seeing you go high-mobility build, metal and other heavy armors, which one other thing good Tailoring is useful for - is not an option due to high Armor Penalty, too.
Biology - 10 points at level 1 for one of mentioned perks, and 10 more by level 2 if you plan to make Toxic Gas grenades. It much depends on playstyle though; overall these are hard to use for a melee build, for obvious reason. Also requires 20 in Chemistry iirc. Going any higher - i doubt your build should, 'cause of mediocre Int, so it'd be another big skill points investment for rather limited gains. Gonna go high Int if most / all crafting skills with a combat build are desired, me thinks.
Chemistry - entirely depending how much and which ones grenades are to be used. I say, it's really good to have strong grenades for a melee build - a ranged utility for non-ranged character is double important. I'd sure take Grenadier some time mid-game, possibly even grenade-crit feat later on, and i'd develop Chemistry right, or soon, after Mechanics and Electronics all the way to effective 112 to craft tier 5 grenades. With said feats, they can be real powerful, and sometimes it's really helpful to thin out enemies before going melee 'cause there are just way to many.
