Hi oneballnoa, welcome to SitePoint!
It partly depends on how large/complex the site is, and what the site needs to do. Two very popular options these days are to build your site with WordPress (if the site is reasonably simple and mainly consists of new topcs being posted regularly) or ExpressionEngine (for a larger site with lots of sections where content needs to be added or updated).
What you are looking for is a content management system (CMS) and each web company will have their preferred CMS(s). Perhaps the best thing to do is ask them to show you a demo of the CMS they use and see if you like the look of it. Some are free and some cost quite a bit. ExpressionEngine costs a bit, but it is worth the price, so I'd look for a place that uses that.