only three coins are worth to buy BCH.BTC and ETH.
rest coins are going up like bubble and next day coming down like bubble blast.
which coin is best out of these three coins to buy in January 2020 and hold for one year to see profit.?
Firstly, I think that you're wrong for saying that there are only three viable coins to invest in - that is obviously not true.
There are plenty of coins that have potential to outperform BTC in this upcoming bull market. EOS, Dash, XMR just to name a few. There is no reason to restrict yourself to BCH, BTC and ETH just because they have the largest market caps.
But lets assume that your only choices are these 3 coins. I would certainly not go with Bitcoin Cash as it has no fundamentals or adoption to speak of. BTC should consist the majority of your portfolio since it is after all, the leading crypto with the most long term stability. I would split around 25% of my portfolio into ETH as well, given the fact that it's likely to have a strong recovery against BTC after regression in prices in 2018-19.