To create your own wallet, you should start by downloading the bitcoin client and running it: from there you can make as many new addresses you want which will be stored in your wallet.
From mybitcoin you can then send BTC's to your new address.
For securing your wallet, take a look at the wiki
As for trusting mybitcoin with all your money: that is up to you to decide. Personally, I wouldn't for a couple of reasons:
- I trust myself more to handle my data/wallet safely than I do a third-party.
- Mybitcoin holds accounts for different users, making it a nicer target for crackers: if they manage to break in, they will gain access to a lot of different wallets, not just yours.
If you don't store too much there it shouldn't be much of a problem, but if you put all your life savings there and it ends up lost, then you can only blame yourself for putting all your eggs in the same basket.