I just simply use Bitcoin Core... I mean privacy is the whole point of bitcoins and web-interfaces log ip's and doesn't have something like source code so you never exactly now what's going on. But thats just my opinion and when it is more important for you to accept multiple crypto currencies in one wallet then it might be something for you.
Edit: BUT for Beginners it's of curse better to use services like jaxx.io or blockchain.info because it is simple and your wallet file can't be stolen or deleted or something like that...
The big downside of Bitcoin Core is the huge chuck of files it needs to download and store on your hard/SSD drive.
I had Bitcoin Core on my old computer and indeed you need a lot of space on you harddisk for the donwload. That's why i have bought an external harddisk of 1 TB. I have put everything on this one and now needs a good 100 GB. So i hope to be good for still a lot of years.
Since a few weeks i use also blockchain.info where i have put a small amount, for the moments i want to pay little things with it. I find blockchain.info easy to use, works fast.