Which antibiotic is most effictive for cureing long term uti?

No cure -treatment. The most commonly used antibiotics for treating recurrent urinary tract infections (utis) are Nitrofurantoin (aka macrobid) and trimethoprim/sulfamethoxazole, which are cheap + usually well tolerated. But, it's important to try to learn why utis keep occurring + the doctor may want to do some studies. Also, prevention through good toilet hygiene + fully emptying bladder often enough is also key.
Correct antibiotic. Depends upon which antibiotic bacteria are sensitive to. Bactrim (trimethopri/sulfa), Macrodantin (nitrofurantoin macrocrystals) & Cipro (ciprofloxacin) are all highly effective first line antibiotics unless bacteria are resistant. Culture & sensitivity testing of urine should give the answer. Good luck.