I am curious what the first plants are thought to have been like, what they may have evolved from, and how much earlier (or later) than animals they are thought to have moved to land, if they even started in water like animal-life?
You can have a look to the most basal branches and you may get a pretty good idea of what those early plants looked like.
What we call plants is what we call plantae or Archaeplastida in Latin. This clade contains the red algae and the green algae. Within the green algae are the land plants. In the land plants are the embryophyta which contain all what you think of when talking about plants. Below are a bunch of pictures so that you can get an idea of what the basal branches look like.
(Basal Plantae) Red algae
(Basal Green Algae) Green Algae
(Basal embryophyta) Green Algae > Embryophyta > Hornworts
(Basal embryophyta) Green Algae > Embryophyta > Mosses
You can explore the tree of life by yourself by going on tolweb.org. You can try to find the apple tree, the ladybug of the human by clicking on the links. It is fun and it is good to learn a bit how the tree of life looks like.