There are several Monero wallets currently under development which will be released soon. Ledger, for its part, is apparently working on adding XMR integration. Until that happens, there are a few existing solutions people can check out as well. Always make sure to set up your wallet properly, though.
3. Standard Monero GUI
Although it may not sound all that appealing to use the regular Monero GUI wallet, this project was created specifically to ensure users keep their money safe at all times. After all, the new GUI binaries for the Helium Hydra update were released not too long ago. This wallet can be installed on any operating system one can run these days, including Windows, Linux, and Macintosh. It is a pretty decent wallet that feels pretty lightweight and does the job just fine.
As is the case with any cryptocurrency desktop wallet, users need to take some precautions to properly secure their Monero, though. Setting up a password-protected wallet is of the utmost importance; that much is pretty evident right now. In addition, always make sure you effectively back up your wallet.keys file in multiple ways to avoid any loss of funds if your computer ever experienced any major issues.
2. USB Monero Cold Wallet
Keeping money in a cold wallet solution is highly effective from a security standpoint, especially when dealing with various cryptocurrencies. Given that the value of Monero shot up recently, security should be the number one priority moving forward. Using a cold storage solution can go a long way in this regard, as it is a pretty reliable way to keep money safe from harm.
In the case of the Taushet USB Monero Cold Wallet Generator, it takes about 10 minutes to set up cold storage for your Monero. You will need a few tools as outlined in this post, but it is one of the more secure ways to effectively ensure your money is safe from harm. People who are heavily involved with Monero take the security of their wallets very seriously, as should everyone. There are some other options in the thread linked to above to check out as well.
Although we are personally not a big fan of online wallets, there is a good reason to trust MyMonero. It is a project operated by the Monero developer himself, which means users should not be overly concerned about losing money. Assuming, that is, that you take ample precautions and never store large amounts of money in it. Considering who maintains this wallet, one cannot compare this to an exchange wallet whatsoever.
From a convenience point of view, using MyMonero makes a lot of sense. It is a very popular wallet service as well, which is not entirely surprising. Users will still need to generate a unique password to ensure no one else can breach their online wallet, though. So far, no MyMonero wallet has ever been hacked, but that is partially due to people taking proper security precautions with unique passwords and such.