Service-based website (no eCommerce) that is building off of a pre existing website as well.
You really need to do thorough research when deciding on your website rebuild. There's no real answer. It really just depends on your budget. I would ensure the site is user friendly first. Second, I'd hire an SEO content specialist to follow SEO best practices. And, lastly, I'd incorporate a blog to ensure you're ranking high on SEO in due time. Considering all of this, shop around with a budget of 5k and find your best bang for your buck! You got this!