I felt the same the first time I tried but it honestly takes a few tries to start getting it right. The kind of iron and solder matter a lot; the older ceramic core ones suck and the JBC/pinecil type are much superior. Part of the problem with the ceramic type ones is they have one setting - full blast - and not good temperature control. With a pinecil/JBC you can set the temperature to 300C and expect to get 300C. Too hot and it will boil off the flux before you're done soldering and you just get crud.

In terms of solder, leaded rosin core solder is the best. Don't worry about the lead, as long as you wash your hands. Use a brass sponge type thing to clean the tip frequently to remove crud

For through holes, I'd say get some veroboard off eBay and a bunch of cheap resistors and just start plugging away until you get better. Process is basically - have tip with a bit of solder, poke to pad and pin, put solder into joint and hold 1-3 seconds until solder flows onto pad and pin, remove tip. Putting some flux on in advance helps remove the oxides before soldering

For surface mount (side pads/pins), there are kits with cheap/obsolete/trash components you can just plug away at without fear of messing anything up. Soldering smt is a bit annoying but doable by hand without much training. the process is basically: tin one pad, use tweezers to place part and reheat the solder until the part is in place, solder the rest of the pads, reheat first pad to relieve stress.

Even for large parts, I used to have trouble with unsteady hands. If you are doing smt you really need a microscope or magnifying glass for anything smaller than 0805 - really helps with the visual feedback loop for hand positioning. A microscope significantly improved my dexterity and hand steadiness