I always put one into Restoration, so the heal-self spell is cheaper to cast. When you run out of potions, you use it a lot. I may add a second perk to improve that later.
But thereafter, the only characters who bothered with anything else in that tree were those using mod-added drain health spells that benefited from the Apprentice/Adept/Expert/Master levels.
I've built characters that do melee, but never wear armor, or perk those trees. Most use Alteration instead, but I've even gone without that. An overpowering offense can make defense moot. Primary weapon skill, plus smithing/enchanting to upgrade the weapon itself, can be enough.
I've never perked Speech. Getting better prices is irrelevant, when the merchants have limited cash. You may have to give them more items, but you pick so much stuff up, it's not an issue. Later in the game, when you get the perks that increase their gold, you don't it any more, as you already have more than you can spend.
So if you do One-handed, put all the perks there that you can, and do a few in Restoration, Smithing, Archery, Enchanting when you haven't the levels in One-handed.
Another option is to grab the Bound Sword, and go Conjuration/One-handed with it. It's a decent weapon to start with. You can't use Smithing on it, but there's a perk to increase its damage in the Conjuration tree, which effectively replaces Smithing for that build. Since you're also including Archery, you'd probably transition to Bound Bow later.