Your school should offer free access to many of the main Biochem journals through the library. Many of the best regarded journals are in the Nature publishing group (i.e. Nature, Nature Methods, Nature Medicine, Nature Communications, Nature Chemical Biology, etc) or Cell Press (i.e. Cell, Neuron). Annual Review of Biochemistry is good as well. It also depends on what area of biochem/mol bio you’re interested in. If you want to read about moelcular bio in cancer there are excellent journals devoted solely to that, journal devoted solely to microbio molecular techniques, etc.
If you would like to find articles on a specific topic you can use Pubmed to search many journals for specific articles. If you don’t know how to use Pubmed, you should learn!