Most reliable ISPs provide webspace. You can usually check what "backup" arrangements they have. In the UK, I use UKFSN and PlusNet. Both have occasional outages, and backup hasn't been operational - so if you need 100% you'll need to pay more.
I also use a US provider, mysite4now.com who (as far as I know) have never hiccupped. They were recommended to me by a good friend who knows a lot about this stuff, and swears by them. Price is reasonable, and I've not had any problems.
For security on your website: read up on .htaccess. It works well on the members-only pages of our Group booking website. If the files you want to hide aren't too obvious in the filename, it will take a determined hacker to find them with that in operation.