The urea breath test and stool antigen test are both widely available, low cost, and highly reliable methods of testing. They are not 100% accurate (around 95-98%), however there are some things to consider to increase the odds in your favor.  Urea breath test accuracy can be effected by antibiotic, probiotic, proton pump inhibitor, and also bismuth use.  

     It's a good measure to wait at least 2 weeks or up to 30 days after using any of these products before testing/retesting.  Some stool testing can also be effected by proton pump inhibitors as well.

     Endoscopic examination is the most invasive and high cost testing method, however, it can result in more information gained beyond confirmation of H-Pylori.  It can observe possible ulcers, mucosal atrophy, and other issues due to H-Pylori infection, or possibly even other unrelated conditions.  If such conditions or H-Pylori are believed to be found, a biopsy can be performed, and a small sample for testing can be sent to a laboratory for further study.  Also, a biopsy might be able to tell what specific strain of HP is present, further assisting in selecting treatment options.

 Blood tests are also a low cost, accurate measure for testing, but not necessarily retesting.  They are uneffected by the use of antibiotics or proton pump inhibitors during inital testing, however antibodies in your blood will possibly result in a false positive during a retest, despite being actually H-Pylori negative after treatment.