Thanks for reaching out r_p_sharman,
It sounds like you're having trouble with the speed your messages are being sent. We can help.
While storage can eventually play a role in performance, it doesn't sound like it's the issue from what you've described. Storage becomes an issue when there's not enough for the iOS software to be able to move and manipulate files, which can be compared to moving a dresser or chest of drawers. In the case of moving the furniture, it doesn't matter what you have stored in each drawer, it only matters how much space the dresser takes up in its current location, if you have a truck large enough to move it to the new location, and then space in the new location itself. In much the same way data just needs to be able to fit where it is copied, and have room for the original and a copy to be manipulated without running out of room before being saved inits destination.
Since you have over half of your storage available, you can go on saving your messages. They are very small overall, and would only be an issue if you're already out of space to begin with.
What is more likely is that you are using a weak signal, a slow connection, or trying to send a large attachment.
If you are only noticing this with green SMS messages, then the issue is with the connection you have with your cellular carrier. You can try sending messages in a location with more signal bars, or instead of using cellular data you can connect with a Wi-Fi network instead. If you still don't see improvement, checking with your carrier is a good idea to make sure everything is working as expected with their cellular network.
If you experience these issues with blue iMessages, this means the issue could be with the data connection. You can try using a different Wi-Fi network, or check for interference. This article offers some steps to Resolve Wi-Fi and Bluetooth issues caused by wireless interference.
Give those steps a try, and see if there is any change.
We are here for you.