This is a very practical question that often gets asked around the time of a new expansion launch. Prices for most items are never as high as they are at the beginning of an expansion.
Week 1 prices are crazy
There’s no other word for it. We can head back to my own sales in week one of BfA. I sold Honorable combatant weapons for 96k and a darkmoon deck for 475k. Getting the initial ilvl boost is great so you can take the leap into farming the hardest content as fast as possible. Materials are also in very short supply and will often command high prices.
Recipes are rare so profit margins are through the roof
Overall I spent 3.9 million gold, got 2.8 million gold in sales and increased my AH value by a whooping 5 million gold during the first week of BfA. Darkmoon Decks in particular require dedication to get out in meaningful quantities early. This will often lead to absolutely crazy profit margins for crafting. I was selling the combatant gear for 5-10 times crafting cost while buying all my materials on the AH.
I prefer crafting
My personal opinion is that crafting is better. Working to get recipes and leveling your professions will require both gold and time though. The time you need for unlocking recipes is often time you would want to spend regardless. Doing world quests for rep is useful and you would do emissaries regardless, so you get to double dip your time. The gold requirement is harders, but the sale rate is usually extremely high as well, so you will get your gold back very quickly.
If you want to farm, farm early
If you want to go the farming route you should focus primarily on farming. Unless your level keeps you out of the most profitable gathering areas there is little benefit in leveling if you want to maximize your gold. Also keep in mind that material prices often hit a temporary low during the first day. Expansion launches have typically been late at night on EU. The day following the launch everyone is just leveling their characters and dumping mats on the AH. Then players start hitting max and start buying materials. So don’t sell right away unless you have to.