Joomla and Wordpress are by far the most common and popular website building tools today, and most webmasters, including our own, will recommend one of the two for yours.
How can you choose between the two?
is that you investigate the two thoroughly. Avoid media hype as that is driven by the developers. And your webmaster likely only knows how to use one of the two, but this does not mean it's best for your site and business in the end.
Wordpress is Blogging Software first and Website Software Second.
Wordpress is great for the person who wants to keep it simple yet keep it pretty. Once your webmaster has set things up it's rather easy for you to add update the blog. You can add static pages (About us, Contact) but these are not quite as simple as the blogging aspect as this is where WordPress works around itself. None the less it's overall use is quite simple and by using a template you can really improve the bumps in the road.
So this is a pretty good choice if your requirements will be consistently straight forward. Most webmasters lean toward this software because it's easy to use for them and conversely you.
Joomla is for the more complex site; the site that might need a high membership base for instance.
Joomla is not much harder to update and maintain, but because it does more overall, there is certainly a little more to learn at the outset. Joomla is the software you would consider if you have a site where members should see material that regular visitors do not; sure both can do this but Joomla is made for it. Joomla is also the best choice for a complex shopping system if you prefer proprietary to hosted carts. Joomla has a blog component if you want one as part of your site, but the core design is for website systems.
Either choice can be a good one, but remember...
... your software makes updating pages and information easy, but you still need to keep your site secure - and the most important step of all is in this direction to keep all the software (core and plugins) updated and then backed up.