I might take 3 square wooden posts, about 1.5 meters high, and I need to link them to one or more boards on the bottom, if you propose screws, keep in mind that it has to sit level so they have to be flush. There also needs to be a board on top but that's not nearly as critical as that's not where the lateral force applies I think.
It might have to hold like 6 kg at that height and not break if there is some lateral pressure due to a fat cat propelling off the top of the stand, assuming the base is large and heavy enough not to move in this situation.
At best what I have at my disposal are a drill with drills bits of various sizes and an electric wood saw, and I don't have a way to keep a complex structure still while drilling into it.
Dowels look nice and easy because everything can be drilled separately on a table and then assembled but maybe they are too weak. Self tapping screws are another option, but I'm not sure I can do the countersinking properly and put washers in the hole to prevent it from breaking the board and coming up through it laterally if it's thin and there is a lateral force applied on the post. I'm not using fibreboards but it might be as weak as pine.
Also I don't see how it's possible to keep everything still while screwing in the screw with a drill, the post might rotate around and then it can't be put straight anymore. Still, options can be suggested if you think they're much better.
Glue sounds weak but I have no idea really.
Mortise and tenon and other such stuff - I don't have the tools nor the expertise for that.
Visible metal L-brackets are too ugly.
So the main issue is how deep wood dowels or screws would have to go through the post to be safe, but if you have alternatives do tell me.