I have the Arduino Uno from the Arduino Starter Kit, and I've been working my way through the project book.
I've noticed that the wire connections to the Uno are friction-fit inside the little black slots (don't know the proper term for them, sorry), and I'd like to know if there is a firmer way of connecting the wires, without soldering them.
They seem really small for set-screws, so should I just use a thicker gauge of wire?
And that is why the UNO is inappropriate for most purposes, unless you have a "shield" to mount on it which implements all of the functions and accessories you require. The Nano is the more practical version as it can mount on a standard "solderless breadboard" for prototyping or be soldered to stripboard or your own custom PCB.
If you are going to use the "Dupont" pins to connect to the UNO, then for any design which is finalised to any extent, you want to swap those single housings for multiples to match the sockets on the UNO. Aliexpress item
This greatly improves the stability and durability of the connections; you will note they actually become quite difficult to disconnect which is in this case, a good thing.