Nice, I just started looking into Dogecoin a few days ago. It's been two days now and my wallet is still doing its first sync (about 70%). I also set up a BitCoin wallet and it looks like that'll take weeks to sync. Is this a problem people starting crypto currencies are thinking about? Is it solvable or just how they work?
When you're using an offline wallet like bitcoin-qt or dogecoin-qt, you have to download the entire blockchain for the cryptocurrency. This is what's 'syncing' and can take a while to finish.
You can bypass having to download the blockchain by using an online wallet instead, which solves that specific pain point but they're less secure than your local storage offline wallet.
If you browse /r/dogecoin, you will see that everyone is recommending to stay away from them. They were especially hit by the dogewallet.com hack.
An alternative is using the android wallet. It's been around for some weeks, now, and I didn't see any complains about it. It relies on no central server and it's code is opensource [1], so it can hardly be a scam, I think.
I remember reading something by its author saying that it won't download the whole chain. From my experience, it's faster to sync than qt client, so I suppose it's true. Also, some neat options like disabling sync when not charging and/or not connected to wifi, which make power / bandwidth consumption not a problem.
Anyway, the only official wallet is the qt / cli one [2]. If you want to be safe, it's the one to use. The sync thing may be annoying at first, but it's easily dealt with if you open your wallet once a day, or once in two days (it will take something like five minutes to sync).