Nope changing SMS apps is as easy as installing a replacement and choosing it as your default. Most apps that I'm familiar with will import old threads and the whole operation is seamless and simple. Likely the biggest consideration will be finding an app you can live with, especially after having used the same app for so long.
You may find that you'll have to try a few before finding one that suits you. Free apps will have ads. One app may change the conversation layout in some way that is annoying to you. Another may have a lot of similarities to your old app but won't have that one thing that you really liked about the old app. Or you could find something altogether better, that you love and wonder why you didn't switch sooner. So if you want to be prepared for something, be prepared to try a few.
What carrier are you with? Verizon has one called Messages+, if you're with them, that has a decent spam feature, a decent UI and decent customizations. Google Messages isn't as customizable and doesn't have a few of bells and whistles of other apps, like delayed messages, but it is a solid offering without ads.