If you want to mine Bitcoin with your computer, you are a couple of years late. You would need to buy ASIC, which may or may not pay for the electricity and make profit. Usually may not.
If you want to try out cloud mining.. that's debatable.. some claim that all are ponzi schemes. There are many scams and even if you find a good one, the profit is not great.
So unless you have free power and a warehouse of ASICs, I'd advice you not to mine Bitcoin. If you want some, better buy.


If you want to mine with your computer for learning purpose, I suggest you try to mine some altcoins. Which coin? Pick one with friendly community, for start.
If you want to make profit from mining, you should research and find the altcoin that you cam make profit on. And you have a slight chance if you have a state-of-the-art GPU and you want to mine with it.

After all this, you can search for "best site" for mining, but usually all are the same and the coin list them in its OP.