Basic woodworking tools are different from beginner woodworking tools. For one thing, I don’t like to use the word “beginner” unless I am using it accurately. It’s not a very useful label, in my opinion, because it implies that there are clear-cut and hierarchical steps in your growth as a woodworker. Who wants to return to grade school during his or her valuable shop time? So I only use the word “beginner” when I’m talking about someone who is touching woodworking tools for the first time.
A Jack Handplane is a middle size “bench plane” (i.e. planes that are used so often that they are usually on your workbench). If you’re on a budget a jack plane can temporarily be used in place of other planes that perform specialized functions: (1) rough stock removal (if you buy a second iron/blade and shape it with a curved “camber”), (2) jointing board edges (as long as the board isn’t over 3x the length of your jack plane), and (3) smoothing the boards.
Wooden mallets are mostly used for hitting your chisels when cutting joints (like dovetail joints or chopping mortises). You should never hit a chisel with a metal hammer. Build or buy a mallet that is made of fairly hard wood (e.g. maple, oak, beech wood, etc.), that will feel well balanced in your hand, and that gives you enough weight to chop with your chisels.