As per the title do you download the wallet developed specifically for the coin you want to stake or a multicoin wallet eg Jaxx or MyEtherWallet? Which one is safest to run on my computer 24/7? What would be the pros and cons of each? Thanks
You have to understand how staking works. Some cryptocurrencies out there use POS aka Proof of Stake and with this consensus algorythm you can stake your coins and earn in the long run. Majority of these crypto currencies require you to have your own node. By having your node you have to run it 24/7 in order for your coins to stake. Which means that even if you use some multicoin wallet such as JAXX that has support for your particular coin you won't be able to stake it. MEW has only support for ETHEREUM blockchain which includes only tokens on ethereum, while jaxx support SOME, not all ethereum tokens as well as other crypos on other blockchains.
There are however coins such as Particl that has some system called cold staking where other nodes can stake your coins in a safe way without the need for you to keep the node running, but this is for another topic.