What is the best DoH to start with

What I mean is what one should you level first that will make the others cost less / more efficent???

Im finding weaver pretty good start, plus you craft pretty much all the other crafter/gathering equipment plus casters and a little pug/arc here and there

I started Goldsmith in 1.0 thinking the jewelry would be a great help. Looking back however, I think leveling Blacksmith might be the best to actually start with. You can make the majority of all the crafting tools for the other Doh/DoL classes.

It depends. If you like botany I would suggest weaver, alchemy, or chef. If you like mining you could do blacksmith, armorer, or goldsmith. If you prefer to hunt monsters I'd highly suggest leathercraft because that's how you get the skins for leather.

If you are looking strictly for DoH classes that make other DoH (and DoL) classes better and easier to level, then your starting classes should be weaver, leatherworker and carpenter. Those three combined provide recipes for every equipment slot for both crafters and gatherers, save for tools and jewelry. The former comes from blacksmith, the latter from goldsmith - though I've not seen any goldsmith recipes with relevant stats among the starting recipes. I suppose those will come into play at a higher goldsmith level (I'm guessing 10+).

And I'm not sure that blacksmith is even necessary, considering the class quests throw free tool upgrades at you every five levels.

I'd lvl most or all of the crafting classes to 15 first, for the cross class abilities. But in particular Waste Not Want Not, Hasty Touch, Careful Synthesis and Manipulation are very useful and fairly easy to get to.

Weaver to where you can HQ your own crafting gear would be where I'd start if I was going to do it all over, though what I'd actually do is get botany, level to where i can harvest moko grass and harvest 2-300 of that first. Then I'd HQ myself a set of low level crafting stuff and run carpentry to 15 for rumination, culinarian to 15 for hasty touch (dear god this is expensive... or tediious) and maybe alchemist to 15 for Tricks of the Trade. After that... mining. Copper ore isn't worth mining, but bone chips would be. bronze is cheap enough to buy I wouldn't worry about the cost, but you're going to want to mine your own iron. By now you've got HQ clothes for getting to 15, and the skills (mostly) to HQ tools as well.