Does "Pairing" mean the subject coin can be converted to/from the other coin?
On the exchange listed, yes you will be able to convert it to the paired coins.
Should I choose the one that has the highest liquidity and confidence level?
Highest liquidity means highest trading volume, if the exchange have good reputation in the past, you can use the exchange.
Also, of the exhanges listed for BEAM, the closest I see to what I have is Binance..I have Binance US though...
Binance.com is different from binance US, if binance US is among the listed exchange, you will be able to see it there will low trading liquidity if compared to binance.com with the same coin paired.