With shared hosting you will not be able to secure by yourself. I think you should go with Dedicated hosting as you will get complete access to manage & secure your website.

Do you talk securing it do you mean backup? Sure making backups is no problem and can be conducted any time!

I run a linux based hosting company - we call it webbhotell here in Sweden - and more than happy to help you out with this!

Here are a few points and things that you can consider for this purpose.
> Keep a very secured password
> Change your wordpress login Url
> Install UpDraftPlus and schedule a weekly back up or do that yourself everyweek.
> Install Wordfence and set it properly.
> Never use nulled themes or plugins, Either go for premium ones only or use free ones.

Most of the web hosting companies now provide Free Backup, DDOS Protections, malware protection, Full root Access to configure firewall. If you do not have then search for such web host. change your root password frequently.