>Check current hosting
The difficulty can be getting a true picture of their security, especially if they are secretive or dismissive of any enquiry you make. We can determine if they have installed the latest PHP or other more visible things, but how can you determine if they have upgraded the firmware on their routers, firewalls and other equipment?
There is no simple answer to this but what you are paying for your hosting is often and indication of how good the security will be. The better hosts will generally be very proactive with regard to security.
A cheap host will most likely not use the best hardware / software solutions and may not invest the time in maintaining what they do have.
If you are on shared hosting (one that hosts other websites on the same server and most cheaper hosting uses this model) then all your security efforts might be negated by another user who is lax in security and allows a hacker to get in. It is the responsibility of the host to ensure that each hosting account is insulated from other accounts and if another account is compromised this is contained to that account. Unfortunately this is not always the case.
I had such an experience with one host. It did not matter what I did, including deleting the entire site and rebuilding it from scratch, that site and others on the host were continuously hacked. When I moved all the sites to another host they were no longer hacked.
When people consider cheap hosting they tend to focus on the features and decide if the speed is acceptable. As I have explained security is a real but often hidden consideration.
Another major consideration for me in selecting a host is support, and this is closely related to security. The level and responsiveness of support is usually a good indication of the how pro-active they are with regard to security.
Support is also a critical security consideration in its own right. If your host does not respond to issues in a timely manor then I consider this an important security concern.
Online security is constantly changing and Web hosting companies need to constantly keep up with the changing landscape, and the threats that come with it.
Are you confident your current host is running secure, stable versions of your web server and the software on it?
If you are using a premium host than most likely your host is taking care of this, but if you are a cheaper host then it is time to ask your host about their security.