A geth client only mines a cryptocurrency in a network if you type the command
Where eth.accounts[i] corresponds to the account address you want to use while mining. Unless you type the above command the geth client will not mine any ethereum or cryptocurrency.
I want to interact from the browser rather than command line. Is that possible with geth Or did I pick the wrong application? If not geth please suggest another OR combination of others.
If you want a user interface to interact with the chain you can use the official client by ethereum foundation available here which provides a good interface for the same.
Also how much will it take to start geth completely so that I can run commands. I start node by the following command
$ go-ethereum/build/bin/geth --rpc --rpccorsdomain "*"
By using above command you are starting a full node in the network. The full node will first download the whole blockchain from the genesis block, recompute e each and every transaction in the blockchain, create the whole database(state-trie) for the same. This will take at least a couple of days or weeks to fully synchronize with the network. The synchronization process will start as soon as you connect with a peer in the network.
Additionally if you want faster starting time, you may consider using
$go-ethereum/build/bin/geth --rpc --rpccorsdomain "*" --syncmode "fast"
$go-ethereum/build/bin/geth --rpc --rpccorsdomain "*" --syncmode "light"
Please do read about what is light and fast syncmode corresponds to.