You cannot do 4 star crafting even with the new gear + max melds + supra as you still fall short of control. Unless you use food or FC buffs to change that however that's frowned upon because you lose out on a lot of CP which is really important for these crafts.
In terms of the pathway you should go to get to 4 star, what I did was the offhand for BSM first. Since this is a 3 star craft made by BSM, I just used it to make it's own offhand, thus helping me later on when I have to make all the other offhands. I also made Carpenters offhand, since they make GSM and WVR tools.
The first things you want to bring up to 4 star are Weaver and Leatherworker to make the most profit/artisan gear immediately.
So the order of things I think assuming you can already do 3 star crafts for all these:
BSM Offhand HQ
CRP Offhand HQ
WVR Offhand HQ
Work on Turn in tools for WVR Books
Meld out your offhand to reach stat requirement (do research on this beforehand to not screw yourself later, make it future proof!)
Make 4 star WVR Artisan Gear HQ.
LTW Offhand HQ
Work on Turn in tools for LTW Books
Meld out offhand to reach stat requirement.
Make 4 star LTW Artisan Gear HQ
Work on CRP turn in tools.
Meld out offhand to reach stat requirements.
Make 4 star CRP Artisan Gear HQ.
I know you said you only wanted to do make offhands and be a 4 star LTW. To be successful at 4 star LTW, ideally you want to pursue all of the artisan gear as this will give you more stat options later. If like you said, you don't have big money at hand, then you should make all this gear yourself or if you want to save time, find someone to craft it for you if you supply the mats. This will reduce the grind up to 4star LTW as you now eliminate the need to do WVR and CRP 4 star.
So off your opening post, you want to bring BSM and CRP to 3 star at the minimum, LTW to 4 star. If you want to make all this gear yourself though(artisan gear used for high end crafting), you now need to bring CRP to 4 star and WVR to 4 star.