Since we're not taking any combat perks in the archery or one-handed tree (until we reach lvl 50+) the only way to increase our damage output is to use fortify weapon skill potions and enchantments. There's probably only a need to level both crafting skills if you are playing on difficulties above Adept. Otherwise you could just pick whichever one you like better and be fine.
Oh, and don't feel obligated to train both skills at the same time. I focused primarily on Alchemy early on and didn't start leveling Enchanting until around level 25 (on Master Difficulty) because fights started to take too long if I wasn't constantly chugging potions. By that point I think Alchemy was already in the high 70s or low 80s. I didn't push it to max level until much later (close to level 50).
Since we're not taking any combat perks in the archery or one-handed tree (until we reach lvl 50+) the only way to increase our damage output is to use fortify weapon skill potions and enchantments. There's probably only a need to level both crafting skills if you are playing on difficulties above Adept. Otherwise you could just pick whichever one you like better and be fine.
Oh, and don't feel obligated to train both skills at the same time. I focused primarily on Alchemy early on and didn't start leveling Enchanting until around level 25 (on Master Difficulty) because fights started to take too long if I wasn't constantly chugging potions. By that point I think Alchemy was already in the high 70s or low 80s. I didn't push it to max level until much later (close to level 50).