Alchemy

1 to 300 = 125g

300 to 375 = 240g

Total Cost = 365g

Blacksmithing

1 to 300 = 883g

300 to 375 = 3324g

Total Cost = 4207g

Enchanting

1 to 300 = 726g

300 to 375 = 4116g

Total Cost = 4842g

Engineering

1 to 300 = 231g

300 to 375 = 2516g

Total Cost = 2747g

Jewelcrafting

1 to 300 = 231g

300 to 375 = No Price Yet (really can’t bothered to work it out at the moment)

Total Cost = 756g

Leatherworking

1 to 300 = 171g

300 to 375 = 1773g

Total Cost = 1944g

Tailoring

1 to 300 = 240g

300 to 375 = 1141g

Total Cost = 1381g

So Alchemy is the cheapest to level all the way from 1 to 375, by a long way. I expected that, so no surprise there.
Enchanting is the most expensive, followed by Blacksmithing. I’m not really surprised, seeing as this would be the cost if bought every single mat off of the AH.
But realistically you’re not going to do that. An enchanter will DE a lot of those mats and a Blacksmither will mine a lot. In fact about 75% of the cost for levelling Blacksmithing is the primals required to get from 360 to 375. 75% of the cost for 15 points!! But if you got the felsteel plans, you could knock off over 3,000g off of the cost of levelling BS.
I didn’t do JC 300 to 375 as it varies way too much. You could spend as little as 100g or as much as 5,000g.
So to my mind, Engineering is the most expensive to level as there are not a lot of options for cutting costs, except for mining endlessly to gather the mats needed.