I think the best thing you can do right from the start is to research your host first. Take a look at the recorded history of issues, and see what you can find on the web about what others are saying about that company. You have to remember though, you will find very unhappy people who will say very unhappy things about every host, no matter what. Even though a hosting service may have had issues, it doesn't mean they are a bad bet. It happens to everyone sooner or later. You have to look at how they responded to the issue, as much as why it happened in the first place. Run that stuff through a logic filter before you make a decision. A good indication is how willing your hosting company is to answer your questions, and if they seem to be willing to work with you, and really want your business.
Learn about the correct file and folder permission for your environment. Being on a shared server is very different from being on a dedicated server. Don't be afraid to ask your host - or anyone else - about these things, and research their answers if you think you should.
Learn how, and be diligent about, keeping your own pc and the tools you use to manage your site (ftp clients, usernames, passwords, etc...) secured and free from password harvesting infections and malware in general.
Keep up to date with the most recent security and bug-fix releases for wordpress. I can't stress this enough. Stay on top of it. Also make sure that you make scheduled, regular backups of your database and all of your files. You would be surprised how many people just don't do this. It really can be a major life saver.
Be cautious when using third part themes, plugins, applications, scripts, add-ons, etc... do the research first. If it's a bad idea, you can bet someone has posted something related to it somewhere. Keep your plugins and themes up to date.
Read all the resources you can find. Nothing is 100% sure, but there is no reason why you shouldn't look out for yourself (and your readers and visitors) first, by using all of the tools at your disposal.
Good place to start: Hardening WordPress