I can not understand where will be my blockchain store wallets public addresses for transactions between users. Should I use helpful database like a MongoDB or MySQL for these purposes?
if you're talking about the blockchain of bitcoin, it doesn't actually store public addresses
all nodes use the same standard of LevelDB to store all transaction data, built from raw blocks
if you're talking about the blockchain explorer, you can use the 3 database mentioned by ETFbitcoin
then create your own database for easier implementation for displaying on the web
so web user can search an address and you can easily list all transactions of that address