In a few words:

Software wallets (like BitcoinQT) generally involve downloading the blockchain and are a bit harder to use and understand, but are ultimately safest because you alone are controlling your coins. I wouldn't recommend them for a beginner but they have very important advantages to the others.

Mobile wallets I believe refer to wallets you can use from your cell phone; I don't use any of these so I'm not familiar with them.

Web wallets don't involve downloading anything at all, but ultimately you are not holding your own coins, somebody else is holding them for you, so you have to trust that the person/company running the web wallet won't run off with your coins (which has happened many times).

I recommend blockchain.info's web wallet for any small (say under $200USD equivalent) amount of bitcoin, but I recommend reading a lot more and doing your own research before choosing a wallet, web or otherwise; it's up to you to decide who you trust.