
Hello! Congratulations on 50 Weaver! Definitely getting the rest of your crafters to 15, Culinarian to 37, and Carpenter to 50 will really help you, so that's great! Then from there, level up in whatever order suits your needs.
Personally, I found that leveling up all your classes simultaneously through daily Grand Company turn-ins and Ixali Beastmen quests is really beneficial while you concentrate on one crafter with Levequests. This takes some pressure off in the long run, and it helps since many recipes use ingredients crafted by other crafters. You can even just buy the turn-in item off the market if it's convenient/cheap. Remember, turning in HQ items nets more experience, and eating food can help too! Your Grand Company also sells Engineering Manuals for crafting experience.
Doing Botany and Mining Grand Company turn-ins is also nice, since it means less spending gil on materials as you are able to gather more things! This also means you can make Botany/Mining retainers, which are nice when you're too lazy to go gather more materials or crystals.
For cross-class skills, I think it really depends on what your end goal is. At level 50, you can get away with HQing 2-star recipes with only level 15 cross skills. But if you plan to go for 3-stars, Byregot's Blessing, Steady Hand 2, Ingenuity 2, Careful Synthesis 2, and Comfort Zone save you a lot of trouble. Innovation is a good skill, but I wouldn't say it is essential until getting 4-star. Piece by Piece and Reclaim see much more use when you aim to go to 4-star. Waste Not 2 isn't particularly useful compared to the others.
I found it helpful to get Leatherworker, Weaver, Goldsmith, and Blacksmith up just because you can craft/meld most of your own crafting gear (and sell it for gil!). Goldsmith and Leatherworker also help for desynthesis.
This is a pretty comprehensive, although long, crafting guide for everything up to 4 star, which I found particularly helpful. This reddit thread, this thread, and this thread also have some good tips, and are a shorter read.
Good luck, and happy crafting!
Personally, I found that leveling up all your classes simultaneously through daily Grand Company turn-ins and Ixali Beastmen quests is really beneficial while you concentrate on one crafter with Levequests. This takes some pressure off in the long run, and it helps since many recipes use ingredients crafted by other crafters. You can even just buy the turn-in item off the market if it's convenient/cheap. Remember, turning in HQ items nets more experience, and eating food can help too! Your Grand Company also sells Engineering Manuals for crafting experience.
Doing Botany and Mining Grand Company turn-ins is also nice, since it means less spending gil on materials as you are able to gather more things! This also means you can make Botany/Mining retainers, which are nice when you're too lazy to go gather more materials or crystals.
For cross-class skills, I think it really depends on what your end goal is. At level 50, you can get away with HQing 2-star recipes with only level 15 cross skills. But if you plan to go for 3-stars, Byregot's Blessing, Steady Hand 2, Ingenuity 2, Careful Synthesis 2, and Comfort Zone save you a lot of trouble. Innovation is a good skill, but I wouldn't say it is essential until getting 4-star. Piece by Piece and Reclaim see much more use when you aim to go to 4-star. Waste Not 2 isn't particularly useful compared to the others.
I found it helpful to get Leatherworker, Weaver, Goldsmith, and Blacksmith up just because you can craft/meld most of your own crafting gear (and sell it for gil!). Goldsmith and Leatherworker also help for desynthesis.
This is a pretty comprehensive, although long, crafting guide for everything up to 4 star, which I found particularly helpful. This reddit thread, this thread, and this thread also have some good tips, and are a shorter read.
Good luck, and happy crafting!