For starters, it has always been my opinion to load up on accuracy regardless of the melee job even with "decent" accuracy. At your level, there isn't too many options and some of them are very expensive (PCC), but for the ones you can afford, they are well worth the buy.
As a THF, you will need to stand out. The best way to do that is to be the best at your job and that means having the best of gear possible since you need to overshadow those other generic melee who can get away with natural job stats and auto attack. Use the level 14 hands armor with +3 accuracy (I used those to basically end levels), Spike Necklace (DEX will help acc some), Venerer's, when you can afford them either Woodsman or Sniper's, +attack earrings (Use HQ, they aren't very expensive usually and they help you stick out more for future invites), HQ daggers (don't bother with swords, they lack skill and 1skill = 1 att and 1 acc) which are also great sources of acc/attack, and various other armors for +attack (I preferred +attack because I am a mithra). Start off with making two macros, 1 for full DoT gear which should be loaded with acc and attack where you can get it and a seperate macro for SATA+WS gear. If you have a lot of gear, you might need two macros for each or to use extended macros that you can get from windower.
As for actual fights, use /NIN in the case you can't get away without taking damage or there is AoE that shadow will take. Otherwise sub WAR, but I rarely got that chance so I doubt you will either. However, at your level, there are very few mobs which move faster than normal speed so you should be able to do a pull very easily without ever taking a single hit. Although, I will admit, I liked taking hits with shadows so I could skill up evasion when I was no longer capped. Acid bolts are your best friend. I think you mentioned having BST levels to around 50ish, use that to skill up. Get some cheap bolts either on AH or from NPC, charm a pet to tank and go to town until you cap it. Once you do and those bolts start landing even if not every mob, you will enjoy it when they do. When I got to 50, it was pre-RNG nerf though so ranged accuracy wasn't a huge issue as it is today; however, with sushi, it should be a lot easier. Acid Bolts also help remove DEF boosts by crawlers which are very common exp mobs for your level.
Try networking. If you see some members regularly, talk to them and see if they plan on having another party next time you are on. Be friendly, start conversations, and all those types of things. Also, you're in TheFlock which has a large amount of BSTs so I would guess there would be at least one 37 NIN or WHM (common BST subs) who wouldn't mind partying with a LS member.
That is all for now; thereis more, but I don't have time to post it. Perhaps some of the other career thieves can post some of the common tricks of the trade.