There isn't much complexity in a normal toilet. It consists of a fill valve, a flap in the tank's bottom, a gasket between the tank and the bowl, a toilet seat that may need replacing occasionally, and a wax gasket between the toilet's bottom and the floor flange. Common issues are with the fill valve and the flap in the bottom. Sometimes the flush handle breaks and requires replacement. All of these problems can be fixed with basic tools. Replacing the flap usually doesn't require any tools. Repair kits, including a fill valve and a new flap, can be purchased for $20 or less at hardware stores or building supply shops.
Modern fill valves have a plastic nut that holds them in place and generally don't stick. However, in the past, metal nuts on metal fill valves were commonly found, which can corrode and may need to be cut off. A hacksaw can be used, but a Dremel with a cutoff wheel is even more effective. I recently came across a fill valve that needed the float rod to be shortened to prevent it from rubbing against the tank's side. This modification can be easily done using either a hacksaw or a Dremel with a cutoff wheel.