Sadly there are significant risks to having valuable information accessible via the internet. Someone with access to your accounts is a huge risk and it can be a huge hassle to deal with what they can do with that access. Email is one of the most critical, there is tons of information you need, and often the email account can be used to get access to many other accounts (obviously financial sites are also critical, as are others). You should set up 2 factor authentication for critical sites.
2 factor authentication is made of up 1 thing you know, and 1 thing you have. So you know your password. The easiest other item is a smart phone (that is the default option for gmail and most places for the thing you have). Some banks and computer networks (intranet access) use security tokens. Either way they give you a code which you then enter after you enter in your username and password.
Gmail offers a app for smart phones that will generate these codes even if you don’t have cell phone service. Also, if you don’t have a smart phone, or lose yours there is a backup thing you can have (pre-printed codes). Make sure you print these and keep them somewhere you can access them (Google suggests your wallet).
With Gmail you will be prompted for your 2nd level authentication if you attempt to access with a computer that has not been authorized previously. If you are using a computer that you logged into your account with and told Google to authorize you will login normally. Every 30 days Google will then have you provide the 2nd level authentication (I think this is right, I might not have it exactly right for when Google asks for 2nd level authentication).
Whatever email account you have I would strongly recommend having 2 factor authentication setup. And you then must be sure that you can gain access. It is a bother but you need to make sure you understand the process and understand how to cope with issues (losing your smart phone, etc.).
Once you setup your account for 2 factor authentication make sure you add a secondary phone number backup (in case you lose your phone or it is stolen). And make sure you print out the backup code.
Process: