Oh boy, time to dust off my expired IPC 610-A cert. If that’s the cheap lead free solder that comes free with soldering irons or unbranded from ebay/amazon that’s about par for the course and you’ll struggle to get better - the joints will always look a bit crusty. High end lead free solder is better but also can be very expensive. As Neil says, traditional 60/40 or 63/37 tin-lead is way better if you can source it (RoHS regs make it difficult but it’s still possible). Some folks are scared of the lead, but I’ve been soldering regularly and almost exclusively with leaded solder since I was about 11 (that’s over 20 years!), and a blood test showed that I (surprisingly, for anyone who knows me) do not have any detectable lead in my system. The person who gave me the results over the phone was surprised we even bothered with a blood test, as she only ever dealt with people who did things like shovelling powdered lead and standing over casting crucibles!
I would also recommend using flux, specifically no-clean flux in a pen dispenser. I like the RS own-brand or Chemtronics and would probably avoid generic stuff. Once you’re done with your joints you can splodge some flux on there and reflow the joint, taking care not to move it while it cools down. The flux will help things flow properly if they weren’t already and if you have any joints that have been overcooked that look like Sonic the Hedgehog on a bad hair day it’ll reflow into a nice little conical solder joint. Don’t breathe the fumes though - they’ll do more damage than the lead.
Finally, if you’re struggling with shaky hands I recommend a combination of those croc-clip “helping hands” soldering stands, masking tape, and blu-tack. With those three items you can jig up pretty much anything on the bench ready to solder, then roughly slap some solder on and let the surface tension do the work. Again, flux is super helpful here if you need a second go at a joint.
