If you're looking for a testing blockchain with a graphical interface, Ganache (previously TestRpc) is for you. It's an in-memory blockchain (think of it as a blockchain simulator) that runs locally. 

Download and install it from the official Ganache repository (https://github.com/trufflesuite/ganache/releases) for the appropriate version for your OS. 

When you run Ganache, you will get a graphical screen showing some details about the server, the blocks created, transactions, and a list of created accounts, each loaded with 100 ether:

To interact with Ganache, you can use Remix, but this time, you have to specify a new web3 provider with Ganache's IP and RPC port; for example, http://localhost:7545 (if you have connection troubles, try to use Remix over HTTP, not HTTPS):

Once Remix is connected to Ganache, deploy your smart contract as you did earlier and start bidding through Remix. In Ganache's interface, you'll be able to visualize the transactions and the created blocks:

If you think Ganache is enough for you, you can stop here and jump directly to the Running the auction DApp section, in order to run the auction DApp using Ganache. However, if you're interested in learning about other possible deployment environments so you can choose the suitable one for you, continue reading.