Each BP runs one or more eos nodes and each node has to have identical blockchain data.
You can run a full node too like anyone else.
For more information I would recommend you do some reading on dev portal.
https://developers.eos.io/

EOS Wiki
https://github.com/EOSIO/eos/wiki

and StackExchange for Q&A
https://eosio.stackexchange.com/

Also there is a EOS Resource Planner you can use to calculate your resource needs.
https://www.eosrp.io/