Best ASIC Bitcoin Miner
Generally, it's not worth your time and effort to mine at home! (Some exceptions may apply.)
Age of ASIC mining
CPU mining has been unprofitable since 2011, GPU mining just slightly later.
Today, ASICs rule mining. The Bitcoin network has more than 1.7 Ehash/s (Oct 2016) now which is 1, 700, 000, 000, 000 Mhash/s. Your graphics card will be running full blast to churn out a few hundred Mhash/s, your CPU maybe a few dozen.
With CPU or GPU you will never collect a sufficient balance with a mining pool that you could even get paid out. It's a waste of time, even if you don't pay for power.
Mining has gone big scale
Meanwhile, ASIC mining has gone industrial. Corporations are building mining centers in regions with very cheap power, and filling them with millions of USD worth of ASIC miners. Greater mining power in one hand does have some slight advantages which adds to their more efficient processes.
Finally, ASIC miners have been catching up quickly technologywise: Every few months new chips get announced moving the scale down a few more nm. Currently, we are reaching 16nm technology (Oct 2016), which is already pretty close to the general state of the art. The problem with that is that every step of miniaturization comes with a leap in power efficiency, quickly obsoleting older generations of ASICs. Chances are that your investment will outdate before it pays for itself – even when you are just looking at cost of acquisition and have no cost of power.
Mining profits tend to zero
The mining market tends to reach an equilibrium: While it is very profitable to mine, there is room for investments. The additional mining power increases the difficulty for all which in turn reduces the profitability. When the difficulty rises, it drives out the least cost efficient mining operations, in turn increasing the profitability of the remaining miners. If you're not in a particularly advantageous position, you will be quickly pushed out of the market.
If you're not paying for your power, someone else is
Anyway, if you're "not paying for your power", because it's included in rent (e.g. in a dormitory), you're either privatizing profits by socializing costs, i.e. stealing from your neighbors, or you'll be paying for it next year when your landlord increases your rent to cover the higher power bill.
If you produce a power surplus or use the ASIC to replace electric heating, hey, you might be one of that exceptions I mentioned going in.
There might be some altcoins that can still be profitably CPU/GPU mined and traded for Bitcoin thereafter, but I am not sure whether even they are worth it when you factor in your time investment.