I would like to store some bitcoins on a software wallet. But it seems like there are quite a few of these and new ones coming up all of the time.
For a newcomer like me can someone suggest which are the most popular?
It depends on your needs.
If you have enough resources (internet bandwidth, RAM, processor speed, and non-volatile storage) then you can run a full node such as Armory or Bitcoin Core.
If you only need an SPV wallet, then I'd suggest MultiBit.
Electrum is also popular.