Up to you really. Once you start buying bag upgrades and horse saddlebag upgrades you shouldn't have too many inventory issues - I've comfortably done Blacksmithing, Woodworking and Clothier on one character (only using 1 set of motifs that way) and Provisioning and Enchanting on another.
If you're planning on leveling two characters concurrently though definitely do it on a second character as long as you're willing to transfer materials. I'm not sure if they changed it since about a year ago but I had Provisioning maxed by just level 20! I think back then the perks that increased the amount of food/drink you make per batch actually multiplied your experience as well.
Up to you really. Once you start buying bag upgrades and horse saddlebag upgrades you shouldn't have too many inventory issues - I've comfortably done Blacksmithing, Woodworking and Clothier on one character (only using 1 set of motifs that way) and Provisioning and Enchanting on another.
If you're planning on leveling two characters concurrently though definitely do it on a second character as long as you're willing to transfer materials. I'm not sure if they changed it since about a year ago but I had Provisioning maxed by just level 20! I think back then the perks that increased the amount of food/drink you make per batch actually multiplied your experience as well.